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Sheet</h1> <div id="bodyContent" class="mw-body-content"> <div id="siteSub">From OeisWiki</div> <div id="contentSub"><div id="mw-fr-revisiontag" class="flaggedrevs_quality flaggedrevs_stable_synced plainlinks noprint nomobile"><img class="flaggedrevs-icon" src="/w/extensions/FlaggedRevs/frontend/modules/img/3.png" alt="This is a quality version of this page" title="This is a quality version of this page" />This is the <a href="/wiki/Help:Page_validation" title="Help:Page validation">stable version</a>, <a rel="nofollow" class="external text" href="https://oeis.org/w/index.php?title=Special:Log&type=review&page=Style_Sheet">approved</a> on <i>7 February 2025</i>.<a id="mw-fr-revisiontoggle" class="fr-toggle-symbol" style="display:none;" title="show/hide details" >(+)</a><div id='mw-fr-revisiondetails'> <span class='fr-marker-60'><strong>Readability</strong>: <span class='fr-text-value'>Approved </span> </span> </div></div> </div> <div id="jump-to-nav" class="mw-jump">Jump to: <a href="#column-one">navigation</a>, <a href="#searchInput">search</a></div>  <div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><p><br /> </p> <div style="text-align: center; font-size: 32px;"><b>Style sheet for contributors</b></div> <p><br /> </p> <div id="toc" class="toc"><div class="toctitle"><h2>Contents</h2></div> <ul> <li class="toclevel-1"><a href="#Style_sheet_for_contributors_to_the_OEIS"><span class="tocnumber">1</span> <span class="toctext">Style sheet for contributors to the OEIS</span></a></li> <li class="toclevel-1 tocsection-1"><a href="#Format_of_entries_in_the_OEIS"><span class="tocnumber">2</span> <span class="toctext">Format of entries in the OEIS</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="#A-number"><span class="tocnumber">2.1</span> <span class="toctext">A-number</span></a></li> <li class="toclevel-2 tocsection-3"><a href="#Name"><span class="tocnumber">2.2</span> <span class="toctext"><span>Name</span></span></a></li> <li class="toclevel-2 tocsection-4"><a href="#Data"><span class="tocnumber">2.3</span> <span class="toctext"><span>Data</span></span></a></li> <li class="toclevel-2 tocsection-5"><a href="#Offset"><span class="tocnumber">2.4</span> <span class="toctext"><span>Offset</span></span></a></li> <li class="toclevel-2 tocsection-6"><a href="#Comments"><span class="tocnumber">2.5</span> <span class="toctext"><span>Comments</span></span></a></li> <li class="toclevel-2 tocsection-7"><a href="#References"><span class="tocnumber">2.6</span> <span class="toctext"><span>References</span></span></a></li> <li class="toclevel-2 tocsection-8"><a href="#Links"><span class="tocnumber">2.7</span> <span class="toctext"><span>Links</span></span></a></li> <li class="toclevel-2 tocsection-9"><a href="#Formula"><span class="tocnumber">2.8</span> <span class="toctext"><span>Formula</span></span></a></li> <li class="toclevel-2 tocsection-10"><a href="#Example"><span class="tocnumber">2.9</span> <span class="toctext"><span>Example</span></span></a></li> <li class="toclevel-2 tocsection-11"><a href="#Maple"><span class="tocnumber">2.10</span> <span class="toctext"><span>Maple</span></span></a></li> <li class="toclevel-2 tocsection-12"><a href="#Mathematica"><span class="tocnumber">2.11</span> <span class="toctext"><span>Mathematica</span></span></a></li> <li class="toclevel-2 tocsection-13"><a href="#Programs"><span class="tocnumber">2.12</span> <span class="toctext"><span>Programs</span></span></a></li> <li class="toclevel-2 tocsection-14"><a href="#Cross-references"><span class="tocnumber">2.13</span> <span class="toctext"><span>Cross-references</span></span></a></li> <li class="toclevel-2 tocsection-15"><a href="#Keywords"><span class="tocnumber">2.14</span> <span class="toctext"><span>Keywords</span></span></a></li> <li class="toclevel-2 tocsection-16"><a href="#Author"><span class="tocnumber">2.15</span> <span class="toctext"><span>Author</span></span></a></li> <li class="toclevel-2 tocsection-17"><a href="#Extensions"><span class="tocnumber">2.16</span> <span class="toctext"><span>Extensions</span></span></a></li> <li class="toclevel-2 tocsection-18"><a href="#Status"><span class="tocnumber">2.17</span> <span class="toctext"><span>Status</span></span></a></li> </ul> </li> <li class="toclevel-1 tocsection-19"><a href="#A_typical_entry"><span class="tocnumber">3</span> <span class="toctext">A typical entry</span></a></li> <li class="toclevel-1 tocsection-20"><a href="#How_many_terms_do_we_need.3F"><span class="tocnumber">4</span> <span class="toctext">How many terms do we need?</span></a></li> <li class="toclevel-1 tocsection-21"><a href="#Signing_your_name_when_you_contribute_to_an_existing_sequence"><span class="tocnumber">5</span> <span class="toctext">Signing your name when you contribute to an existing sequence</span></a></li> <li class="toclevel-1 tocsection-22"><a href="#Email"><span class="tocnumber">6</span> <span class="toctext">Email</span></a> <ul> <li class="toclevel-2 tocsection-23"><a href="#Don.27t_include_your_email_address"><span class="tocnumber">6.1</span> <span class="toctext">Don't include your email address</span></a></li> <li class="toclevel-2 tocsection-24"><a href="#Sending_email_to_an_author_or_editor"><span class="tocnumber">6.2</span> <span class="toctext">Sending email to an author or editor</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-25"><a href="#Spelling_and_notation"><span class="tocnumber">7</span> <span class="toctext">Spelling and notation</span></a> <ul> <li class="toclevel-2 tocsection-26"><a href="#Non-ASCII_characters"><span class="tocnumber">7.1</span> <span class="toctext">Non-ASCII characters</span></a></li> <li class="toclevel-2 tocsection-27"><a href="#Grammar"><span class="tocnumber">7.2</span> <span class="toctext">Grammar</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-28"><a href="#Common_mistakes_in_English"><span class="tocnumber">8</span> <span class="toctext">Common mistakes in English</span></a></li> <li class="toclevel-1 tocsection-29"><a href="#Technical_definitions"><span class="tocnumber">9</span> <span class="toctext">Technical definitions</span></a></li> <li class="toclevel-1 tocsection-30"><a href="#Sequences_with_conjectured_terms"><span class="tocnumber">10</span> <span class="toctext">Sequences with conjectured terms</span></a></li> <li class="toclevel-1 tocsection-31"><a href="#If_you_have_solved_a_famous_open_problem"><span class="tocnumber">11</span> <span class="toctext">If you have solved a famous open problem</span></a></li> <li class="toclevel-1 tocsection-32"><a href="#See_also"><span class="tocnumber">12</span> <span class="toctext">See also</span></a></li> </ul> </div> <h2 style="font-size: x-large;"><span class="mw-headline" id="Style_sheet_for_contributors_to_the_OEIS">Style sheet for contributors to the OEIS</span></h2> <h2><span class="mw-headline" id="Format_of_entries_in_the_OEIS">Format of entries in the OEIS</span></h2> <p>Entries in the OEIS have a rigid format. Each entry contains some or all of the following fields. </p> <h3><span class="mw-headline" id="A-number"><a href="/wiki/A-number" class="mw-redirect" title="A-number">A-number</a></span></h3> <p>The A-number is an A followed by six digits (until we reach <a href="https://oeis.org/A999999">A999999</a>). Example: </p> <dl><dd> <b><a href="https://oeis.org/A005132">A005132</a></b></dd></dl> <ul><li> This is the absolute catalog number of the sequence. </li> <li> Some sequences also have a 4-digit <a href="/wiki/M-number" class="mw-redirect" title="M-number">M-number</a>, such as M1459, which is the number they carried in "<a href="/wiki/The_Encyclopedia_of_Integer_Sequences" title="The Encyclopedia of Integer Sequences">The Encyclopedia of Integer Sequences</a>" by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, CA, 1995.</li> <li> Some older sequences also have a 4-digit <a href="/wiki/N-number" class="mw-redirect" title="N-number">N-number</a>, such as N0577, which is the number they carried in "<a href="/wiki/A_Handbook_of_Integer_Sequences" title="A Handbook of Integer Sequences">A Handbook of Integer Sequences</a>", by N. J. A. Sloane, Academic Press, NY, 1973.</li></ul> <h3><span class="mw-headline" id="Name"><span class="anchor" id="Name"></span><span class="smallcaps" style="font-variant: small-caps;">Name</span></span></h3> <p>This gives a brief description or definition of the sequence. Example: </p> <dl><dd> <b>The even numbers.</b></dd></dl> <ul><li> In the description, a(n) denotes the n-th term of the sequence and n is a typical subscript. <dl><dd> Example: a(n) = a(n-1) + a(n-3).</dd></dl></li> <li> In some cases however the definition will describe a typical term k in the sequence. <dl><dd> Example: Numbers k such that k and k+1 have the same number of divisors.</dd></dl></li> <li> Use the notation and spelling as described <a href="#Spelling_and_notation">below</a>.</li> <li> Avoid vanity: do not name the sequence after yourself (or your family members, your friends, etc.). </li> <li> Prefer concise mathematical definitions when possible.</li> <li> When submitting a sequence, once a name has been entered, it might be necessary to make small changes, but for a complete change, e.g., if the original sequence was aborted or withdrawn, do not use the same A-number; please ask for recycling and request a new A-number.</li></ul> <h3><span class="mw-headline" id="Data"><span class="anchor" id="Data"></span><span class="smallcaps" style="font-variant: small-caps;">Data</span></span></h3> <p>This field gives the beginning (at least 4 terms) of the sequence. Example: </p> <dl><dd><b>1, 1, 1, 2, 3, 5, 9, 32, 56, 144, 320, 1458, 3645, 9477, 25515, 131072, 327680, 1114112</b></dd></dl> <ul><li> Ideally this field should give enough terms to fill about three lines on the screen—maybe 260 characters including [decimal] digits, signs, commas and whitespaces (spaces and newlines; DO NOT USE tabs). (In the above example no more terms were known when the sequence was created.) </li> <li> The sequence may contain negative integers—if the sequence is known to contain negative integers it should be labeled with the Keyword "sign" (i.e., signed sequence); if the sequence is known NOT to contain negative integers it should be labeled with the Keyword "nonn" (i.e., nonnegative sequence). </li> <li> When entering a sequence, you may separate the terms by commas or spaces.</li> <li> The entries must be integers—represented with base-10 digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.</li> <li> If the terms are fractions, then the numerators and denominators should be entered as separate sequences, labeled with the Keyword "frac", and with cross-references connecting the two sequences.</li> <li> Only sequences that are well-defined and of general interest should be submitted.</li> <li> If every second term is zero (A, 0, B, 0, C, 0, D, 0, E, ...) then normally we omit the zeros and list the sequence as A, B, C, D, E, ...</li></ul> <h3><span class="mw-headline" id="Offset"><span class="anchor" id="Offset"></span><span class="smallcaps" style="font-variant: small-caps;">Offset</span></span></h3> <p>The index of the first term of the sequence. </p> <ul><li> For lists, the offset should generally be 1, but sometimes 0 is allowed. See <a href="/wiki/Examples_of_offsets" class="mw-redirect" title="Examples of offsets">examples</a>. </li></ul> <ul><li> For arrays and triangles, the offset should be the index of the first row. If the triangle is regular (tabl), then the first index's offset usually is also the second index's offset. If this is not the case, the offset of the second index should be given in the name.</li></ul> <ul><li> There is a second part to the offset after a comma, which is the 1-based index of the first term greater than 1 in absolute value. If all terms are -1, 0, or 1, the second part should be 1. <i>You do not need to add this part; the server will calculate it for you.</i></li></ul> <ul><li> Do not repeat the offsets or ranges they imply in the formulas or comments. Only <i>restrictions</i> of the range of validity for a certain formula need to be indicated.</li></ul> <h3><span class="mw-headline" id="Comments"><span class="anchor" id="Comments"></span><span class="smallcaps" style="font-variant: small-caps;">Comments</span></span></h3> <p>Relevant information that would make the sequence name much too long and interesting side facts that don't fit in the other fields. </p> <ul><li> Generally, comments are placed in chronological order, with newer comments placed at the bottom of the field. However (at the discretion of the Editors-in-Chief), the most important comments will be placed first, even if they are out of chronological order.</li> <li> With the exception of comments made by the author at the time the sequence was first submitted, all comments must identify the commenter and the date the comment was made. <ul><li> Therefore there is no need to write in the Extensions field "Added a comment."</li></ul></li> <li> The Comments section is a good place to explain the motivation for a sequence, especially when there are no links.</li> <li> There are several ways to sign a comment (and all comments not part of the original submission should be signed and dated) (<a href="#Signing_your_name_when_you_contribute_to_an_existing_sequence">see below</a>): <ul><li> The preferred format for signing a short comment is "If n is divisible by 3, so is a(n). - _Alonso del Arte_, Dec 01 2011". That is, the comment is followed by a space, a dash, a space, then the name (in the form of a link), then a comma, a space, and the date. If you type four tilde characters (~~~~), the system will automatically replace them with your username (in the form of a link), a comma, a space, and the date, all in the proper format.</li> <li> Short comments can also be written as "Comment from _Alonso del Arte_, Dec 01 2011: If n is divisible by 3, so is a(n)."</li> <li> Another possible format for short comments is "From _Alonso del Arte_, Dec 01 2011: If n is divisible by 3, so is a(n)."</li> <li> For a comment that extends over several paragraphs, the preferred format is: "Comment from _Alonso del Arte_, Dec 01 2011: (Start)" followed (starting on a new line) by the comments, then "(End)".</li></ul></li> <li> If a comment contains an error, it may be corrected in place. In that case the author of the correction adds his or her signature as in the following example: "a(n) = a(n-1) + 2*(n-1). - _Henry Bottomley_, Oct 02 2000 [Corrected by _N. J. A. Sloane_, Jul 18 2010]"</li></ul> <h3><span class="mw-headline" id="References"><span class="anchor" id="References"></span><span class="smallcaps" style="font-variant: small-caps;">References</span></span></h3> <p>References to books, journal papers, and other material not found online. </p> <ul><li> There are often multiple mentions of an article, in both the References and Links sections. This is perfectly normal and often desirable, for many reasons. Different versions of a paper may have appeared on the arXiv or a home page and also in a journal; a preprint version may have been sent to the OEIS and later changed in the course of publication. References to the OEIS may have appeared in one version and then dropped, or vice versa. Formulas may have changed. Please do NOT delete references or links just because they appear to you to be duplicates!</li> <li> Entries should be alphabetized by the last name of the first author listed. For example, there is a book by John Gold and a paper co-authored by Yang Zhang and Sigfrid Aronson as references for a given sequence. The Gold book goes first, then the Zhang & Aronson paper. (Most math papers list authors alphabetically, but if they use a different ordering use it.)</li></ul> <h3><span class="mw-headline" id="Links"><span class="anchor" id="Links"></span><span class="smallcaps" style="font-variant: small-caps;">Links</span></span></h3> <p>Links to journal papers, preprints, illustrations, web pages, and other material: </p> <ul><li> If a paper is available from more than one location, or in several versions, include all the links (within reason)</li> <li> Indicate broken links by "[broken link]" or replace the URL with an archived version</li> <li> Use stable URLs when available</li> <li> Entries should be alphabetized by the last name of the first author, except that <ul><li> The <a href="/wiki/B-files" title="B-files">b-file</a> link is placed at the beginning</li> <li> Index entries are placed at the end</li></ul></li> <li> When the author is unknown, write "Author?"; when the title is unknown, make up a reasonable descriptive title</li> <li> When the author is a named group, use the name of the group: MathOverflow, N. Bourbaki, Wikipedia, etc.</li> <li> When a single source has many links they may be combined. (E.g., several MathWorld articles may be combined into a single line if the Links section grows too large.)</li></ul> <p>Links containing hidden programs: </p> <ul><li> Links may not be used to trigger the execution of programs whose code is contained in the link in compressed and possibly encrypted form. Instead, it is recommended that these programs be uploaded to the OEIS as external files.</li></ul> <h3><span class="mw-headline" id="Formula"><span class="anchor" id="Formula"></span><span class="smallcaps" style="font-variant: small-caps;">Formula</span></span></h3> <p>Formulas for calculating the n-th term of the sequence, generating functions, asymptotics, and so forth. </p><p>See section <a href="#Spelling_and_notation">#Spelling and notation</a> for preferred notation of mathematical formulae. In decimal expansions a formula <kbd>Equals <i>formula</i></kbd> is about the constant, not about the decimal digits a(n). </p> <h3><span class="mw-headline" id="Example"><span class="anchor" id="Example"></span><span class="smallcaps" style="font-variant: small-caps;">Example</span></span></h3> <p>An example of how to find or interpret terms when it is not obvious. </p> <ul><li> In the special case of a constant, give the first few digits of the decimal expansion (usually to the width of the line).</li> <li> In the special case of a table, give the first few rows (or the top-left corner if a rectangular array).</li> <li> Don't give an example that just repeats the definition. The idea is to choose 1 to 3 simple cases, and show your work.</li></ul> <h3><span class="mw-headline" id="Maple"><span class="anchor" id="Maple"></span><span class="smallcaps" style="font-variant: small-caps;">Maple</span></span></h3> <p>A Maple program. </p> <ul><li> Please sign and date your contribution in a comment, using Maple's end-of-line comment syntax, " # ~~~~ ". Or you can start with " # Maple program from ~~~~ ".</li> <li> Programs should be self-contained except in rare cases.</li> <li> If a program is extremely long, consider submitting it as a link and mentioning it in this field.</li></ul> <h3><span class="mw-headline" id="Mathematica"><span class="anchor" id="Mathematica"></span><span class="smallcaps" style="font-variant: small-caps;">Mathematica</span></span></h3> <p>A <a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Wolfram Mathematica</a> program. For much more about Mathematica programs, see <a href="/wiki/Style_sheet_for_Mathematica_programs" title="Style sheet for Mathematica programs">Style sheet for Mathematica programs</a>. </p> <ul><li> Please sign and date your contribution in a comment, using Mathematica's comment syntax, " (* ~~~~ *) ". Or you can start with " (* Mathematica program from ~~~~ *) ".</li> <li> Programs should be self-contained except in rare cases.</li> <li> If a program is extremely long, consider submitting it as a link and mentioning it in this field.</li> <li> Code in the Wolfram Language belongs in this field even if it is executed via Wolfram Alpha.</li> <li> Programs written specifically in the Wolfram Alpha language are strongly discouraged in the OEIS. The reason is that Wolfram Alpha also accepts inputs that are not in the formal Mathematica language. One can ask Wolfram Alpha something like: "sum the squares from 1 to n". The problem is that the interpretation of a query expressed in natural language is difficult, sometimes produces unwanted results, and even when it gives the expected result there is no guarantee that next year the same English sentence will be interpreted in the same way. Since the OEIS is a scientific database, and reproducibility is essential, programs in Wolfram Alpha are discouraged.</li></ul> <h3><span class="mw-headline" id="Programs"><span class="anchor" id="Programs"></span><span class="smallcaps" style="font-variant: small-caps;">Programs</span></span></h3> <p>A program in some language other than Maple or Mathematica. </p> <ul><li> Please sign and date your contribution in a comment.</li> <li> Programs should be self-contained and copy-pastable, except in rare cases.</li> <li> If a program is extremely long, consider uploading it as a file to be stored with the sequence as a link. (You will see a facility for doing this when editing the LINKS section.) Mention it in this field like so: <dl><dd> <pre>(PARI) \\ See Smith link.</pre> using the appropriate symbol for comments</dd></dl></li> <li> Also give the name of the programming language in parentheses at the beginning, like (PARI) or (Perl)</li> <li> Entries are generally chronological, but keep entries written in a given programming language together.</li></ul> <p>Code should be signed unless it was written by the sequence author as part of the original submission. To allow the program to run in case the signature is copied, the signature should be in a comment. The preferred formats for such comments (in languages frequently used in the OEIS), where the block <code>~~~~</code> will be automatically replaced by the user's name and the current date, are: </p> <table class="wikitable" style="margin:0 0 0 2em;"> <tr> <th> Signature </th> <th> Languages </th></tr> <tr> <td> <code># ~~~~</code> </td> <td> GAP, Julia, <a href="#Maple">Maple</a>, Perl, Python, R, Ruby, SageMath </td></tr> <tr> <td> <code>/* ~~~~ */</code> </td> <td> C, Java, Maxima, PARI, Rexx </td></tr> <tr> <td> <code>// ~~~~</code> </td> <td> C++, Java, Magma, MuPAD, Pascal, Rust </td></tr> <tr> <td> <code>(* ~~~~ *)</code> </td> <td> ARIBAS, <a href="#Mathematica">Mathematica</a>, Pascal </td></tr> <tr> <td> <code>' ~~~~</code> </td> <td> BASIC </td></tr> <tr> <td> <code>! ~~~~</code> </td> <td> Fortran </td></tr> <tr> <td> <code>-- ~~~~</code> </td> <td> Haskell </td></tr> <tr> <td> <code>NB. ~~~~</code> </td> <td> J </td></tr> <tr> <td> <code>% ~~~~</code> </td> <td> MATLAB (with the "%" at the start of a line) </td></tr> <tr> <td> <code>\\ ~~~~</code> </td> <td> PARI </td></tr> </table> <p>It is no longer necessary to replace leading spaces with dots, for languages that require indentation: as soon as a line starts with two spaces or more, they will be preserved. </p><p>Note that code in the Wolfram Language belongs in the Mathematica section, not here, regardless of whether it is executed in Mathematica or Wolfram Alpha, and that code in the Maple language belongs in the Maple section. </p> <h3><span class="mw-headline" id="Cross-references"><span class="anchor" id="Cross-references"></span><span class="smallcaps" style="font-variant: small-caps;">Cross-references</span></span></h3> <p>Cross-references to related sequences. This should be a comma-separated list of sequence numbers without repetition, with a space after each comma. </p> <ul><li> You can give extra information, like "Row sums: <a href="https://oeis.org/A000000">A000000</a>, <a href="https://oeis.org/A000000">A000000</a>, <a href="https://oeis.org/A000000">A000000</a>" or "Subsequence of <a href="https://oeis.org/A000000">A000000</a>"</li> <li> When there is no special information to convey, begin the line "Cf. "</li></ul> <h3><span class="mw-headline" id="Keywords"><span class="anchor" id="Keywords"></span><span class="smallcaps" style="font-variant: small-caps;">Keywords</span></span></h3> <p>One or more of a fixed set of standardized keywords. For more information, see the <a rel="nofollow" class="external text" href="https://oeis.org/eishelp2.html#RK">official descriptions of keywords</a>, <a href="/wiki/Clear-cut_examples_of_keywords" title="Clear-cut examples of keywords">clear-cut examples of keywords</a>, or an <a href="/wiki/User:Charles_R_Greathouse_IV/Keywords" title="User:Charles R Greathouse IV/Keywords">essay on keywords</a> (advanced). </p> <h3><span class="mw-headline" id="Author"><span class="anchor" id="Author"></span><span class="smallcaps" style="font-variant: small-caps;">Author</span></span></h3> <p>The author's name and the date of initial submission. Sequences with multiple authors should have multiple names here. This field generally does not change once the sequence is first approved. </p><p>Older sequences may also include the author's email address; when possible, the author's name should be linked instead. </p><p>This field generally represents the person submitting the sequence, even if the sequence was known earlier. For example <a href="https://oeis.org/A000040">A000040</a>, the prime numbers, were known long before they were entered in the OEIS, but the author is still listed as N. J. A. Sloane. </p><p>Note that we do not include acknowledgements of (for example) financial support. </p> <h3><span class="mw-headline" id="Extensions"><span class="anchor" id="Extensions"></span><span class="smallcaps" style="font-variant: small-caps;">Extensions</span></span></h3> <p>This field is to claim credit for additions to the entry that can't be properly acknowledged in other fields. The most common use is to acknowledge more terms for sequences that had only a few previously, e.g., "a(10)-a(24) from _Jan Schuster_, Mar 14 2015". </p> <ul><li> Comments, programs (including Maple and Mathematica), and formulas should be signed (see more about signing <a href="#Comments">above</a> and <a href="/wiki/QandA_For_New_OEIS#Should_I_sign_my_contributions.3F_.28Yes.21.29" title="QandA For New OEIS">in QandA</a>) and thus do not need to be mentioned in this field.</li> <li> Cross-references, links, references, and (usually) examples are neither acknowledged in this field nor signed in place.</li> <li> During the approval process, you do not need to add anything in this field when making changes to the sequence you are creating.</li></ul> <h3><span class="mw-headline" id="Status"><span class="anchor" id="Status"></span><span class="smallcaps" style="font-variant: small-caps;">Status</span></span></h3> <p>A non-editable field that shows the status of the sequence: approved, editing, reviewed, or proposed. </p> <ul><li> When a sequence is edited, the status is automatically changed to "editing"</li> <li> When the status is changed from "editing" to "proposed", the sequence is shown to the Editorial Board for review and approval <ul><li> Do this by clicking "These changes are ready for review by an OEIS Editor" at the bottom of the sequence draft</li></ul></li></ul> <h2><span class="mw-headline" id="A_typical_entry">A typical entry</span></h2> <p>Here is an (abbreviated) example showing the different types of lines in an entry in the OEIS: </p> <ul><li><dl><dd> <a href="https://oeis.org/A000002">A000002</a> Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's.</dd> <dd> (Formerly M0190 N0070)</dd></dl></li></ul> <pre style="font-size: 100%; overflow: auto;"> NAME Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. DATA 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2 OFFSET 1,2 COMMENTS It is an unsolved problem to show that the density of 1's is equal to 1/2. The sequence is cubefree and all square subwords have lengths which are one of 2, 4, 6, 18 and 54. This is a fractal sequence: replace each run with its length and recover the original sequence. - Kerry Mitchell, Dec 08 2005 ... REFERENCES J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 337. E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris. F. M. Dekking, On the structure of self-generating sequences, Seminar on Number Theory, 1980-1981 (Talence, 1980-1981), Exp. No. 31, 6 pp., Univ. Bordeaux I, Talence, 1981. Math. Rev. 83e:10075. ... LINKS N. J. A. Sloane, <a href="/<a href="https://oeis.org/A000002">A000002</a>/b000002.txt">Table of n, a(n) for n = 1..10502</a> J.-P. Allouche, M. Baake, J. Cassaigns and D. Damanik, <a href="https://arxiv.org/abs/math/0106121">Palindrome complexity</a> Michael Baake and Bernd Sing, <a href="https://arxiv.org/abs/math/0206098">Kolakoski-(3,1) is a (deformed) model set</a> ... FORMULA These two formulae define completely the sequence: a(1)=1, a(2)=2, a(a(1)+a(2)+...+a(k))=(3+(-1)^k)/2 and a(a(1)+a(2)+...+a(k)+1)=(3-(-1)^k)/2. - Benoit Cloitre, Oct 06 2003 a(n+2)*a(n+1)*a(n)/2 = a(n+2)+a(n+1)+a(n)-3 (this formula doesn't define the sequence, it is just a consequence of definition). - Benoit Cloitre, Nov 17 2003 a(n+1)=3-a(n)+(a(n)-a(n-1))*(a(b(n))-1), where b(n) is the sequence <a href="https://oeis.org/A156253">A156253</a>. - Jean-Marc Fedou and Gabriele Fici, Mar 18 2010 EXAMPLE Start with a(1) = 1, a(2) = 2. The rule says that the first run (which is a single 1) has length 1, which it does and the second run (which starts with the 2) has length 2, so the third term must be a 2 also and the fourth term can't be a 2, so must be a 1. So we have a(3) = 2, a(4) = 1. Since a(3) = 2, the third run has length 2, so we deduce a(5) = 1, a(6) = 2. And so on. The correction I made was to change a(4) to a(5) and a(5) to a(6). - Labos Elemer, corrected by Graeme McRae MAPLE M := 100; s := [ 1, 2, 2 ]; for n from 3 to M do for i from 1 to s[ n ] do s := [ op(s), 1+((n-1)mod 2) ]; od: od: s; <a href="https://oeis.org/A000002">A000002</a> := n->s[n]; MATHEMATICA a[steps_] := Module[{a = {1, 2, 2}}, Do[a = Append[a, 1 + Mod[(n - 1), 2]], {n, 3, steps}, {i, a[[n]]}]; a] PROG (PARI) a=[ 1, 2, 2 ]; for(n=3, 80, for(i=1, a[ n ], a=concat(a, 1+((n-1)%2)))); a (PARI) a(n)=local(an, m); if(n<1, 0, an=[1, 2, 2]; m=3; while(length(an)<n, an=concat(an, vector(an[m], i, (m-1)%2+1)); m++); an[n]) CROSSREFS Cf. <a href="https://oeis.org/A064353">A064353</a>, <a href="https://oeis.org/A001462">A001462</a>, <a href="https://oeis.org/A001083">A001083</a>, <a href="https://oeis.org/A006928">A006928</a>, <a href="https://oeis.org/A042942">A042942</a>, <a href="https://oeis.org/A069864">A069864</a>, <a href="https://oeis.org/A010060">A010060</a>, <a href="https://oeis.org/A078880">A078880</a>. Cf. <a href="https://oeis.org/A079729">A079729</a>, <a href="https://oeis.org/A079730">A079730</a>, <a href="https://oeis.org/A078929">A078929</a>, <a href="https://oeis.org/A171899">A171899</a>. KEYWORD nonn,core,easy,nice,new AUTHOR N. J. A. Sloane EXTENSIONS Minor edits to example and PARI code made by M. F. Hasler, May 07 2014 STATUS approved </pre> <h2><span class="mw-headline" id="How_many_terms_do_we_need.3F">How many terms do we need?</span></h2> <ul><li> Normally an entry in the OEIS will give enough terms to fill three lines on the screen, about 260 characters including spaces and commas. (Enough to fill three <a href="/wiki/File:Punch_card.jpg" title="File:Punch card.jpg">punched cards</a>, in the old days.)</li> <li> 260 characters is just a guide. If you want to give more, go ahead. We are not traffic cops with our radar guns set to flash red at 261 characters. There is ample space. Try to stay under 500 chars, though.</li> <li> If more terms are available, then the entry may have a <a href="/wiki/B-files" title="B-files">b-file</a>, giving the first 1000 or 10000 or 20000 terms, or more in exceptional cases. The most common size is 10000 terms. The Editors-in-Chief have the final say about what size of b-file is appropriate.</li> <li> If the entry already has about three lines' worth of terms, there is usually no point in adding more terms to the DATA lines -- instead, create a b-file. </li> <li> Generally, the minimum number of terms required is 4.</li></ul> <h2><span class="mw-headline" id="Signing_your_name_when_you_contribute_to_an_existing_sequence">Signing your name when you contribute to an existing sequence</span></h2> <ul><li> You should sign (i.e., add your name & date) when you add something to an existing entry. This is done by appending <code style="white-space: nowrap;"> - ~~~~</code> at the end of the line, which will take care of correctly formatting your name (including the link) and the date. The same information is available in the History section, but it is the standard convention in the OEIS and useful for the reader who does not want to search the history of revisions.</li> <li> If you are adding something that extends over several paragraphs, then rather than putting your name on every line, put <code style="white-space: nowrap;">Comment from _N. J. A. Sloane_, Sep 24 2007: (Start)</code> at the beginning and <code>(End)</code> at the end.</li></ul> <table class="wikitable" style="margin:1em 0 1em 2em;"> <caption> Examples </caption> <tr> <td><pre style="margin:0;"> T(k,n) = n(k-2)((k-2)n^2+1+2n)/2. - _R. J. Mathar_, Jun 12 2008 </pre> </td></tr> <tr> <td><pre style="margin:0;"> Comment from _Paul D. Hanna_, Jun 14 2009: (Start) More generally, if G(x) = exp(p*x*exp(q*x*G(x))), where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!, then g(n,m) = Sum_{k=0..n} C(n,k)*p^k*q^(n-k)*m*(n-k+m)^(k-1)*k^(n-k). (End) </pre> </td></tr> <tr> <td><pre style="margin:0;"> T(k,n) = n(k-2)((k-2)n^2+1+2n)/2. [_R. J. Mathar_, Jun 12 2008] </pre> </td></tr> </table> <h2><span class="mw-headline" id="Email">Email</span></h2> <h3><span class="mw-headline" id="Don.27t_include_your_email_address">Don't include your email address</span></h3> <ul><li> Since 2011, it has been the policy of the OEIS not to display email addresses of contributors.</li> <li> Instead, sign your name by typing four tildes (~~~~) at the end of a line to link to your User Page. This should be automatically converted to your name and date. <ul><li> In comments, examples and formulae, this signature is typically preceded by " - " (space, dash, space), separating it from the (mandatory) period (".") at the end of the comment. (Example: "This is a comment. - ~~~~".) But " [~~~~] " is also acceptable (the signature is inserted between square brackets). In programs, the name and date is either put inside comment delimiters (e.g., "(*...*)" in Mathematica), or (preferably) after a comment-up-to-end-of-line introducing character or characters, if available ("#" in Maple, "\\" in PARI/GP, "//" in C; see <a href="#Programs">above</a> for other programming languages; this allows users to copy/paste the code and a possibly incomplete part of the signature without generating errors when the code is executed).</li></ul></li> <li> See <a href="#Signing_your_name_when_you_contribute_to_an_existing_sequence">above</a> for examples.</li></ul> <h3><span class="mw-headline" id="Sending_email_to_an_author_or_editor">Sending email to an author or editor</span></h3> <ul><li> Provided this person has a user page on this Wiki (and ideally every contributor should have such a page), first go to the OEIS Wiki and log in, then go to the user's page (enter, for example, User:John Doe, in the Wiki search box). Then there should be a link in the Toolbox on the left saying "E-mail this user". Of course, there are many possible reasons why a contributor, even one with a user page, may not have a current email address.</li> <li> You may also leave a message for the user on her or his User Talk page (but again you must first log in to the OEIS Wiki — the Wiki requires a separate login from the main OEIS database).</li></ul> <h2><span class="mw-headline" id="Spelling_and_notation">Spelling and notation</span></h2> <p>The following are the correct spellings for some words and symbols that are commonly mistyped in the OEIS, also the preferred versions of various useful symbols: </p> <ul><li> <b>></b> (not grth)</li> <li> <b>>=</b> (not ≥ or \ge or \geq)</li> <li> <b><=</b> (not ≤ or \le or \leq)</li> <li> <b>!=</b> or <b><></b> for "not equal" (not ≠, .NE., \ne, \neq), e.g., x != y or x <> y.</li> <li> For <b>/</b> write a/(bc), not a/b*c or a/b/c which are ambiguous (see <a href="/wiki/Operator_precedence" title="Operator precedence">operator precedence</a>). For example, don't say 1/6x, say x/6 or (1/6)x. Don't say 1/6 Sum ..., say (1/6) Sum ... . Don't say 1/(1-x)/(1-x^2), say 1/((1-x)(1-x^2)).</li> <li> <b>|S|</b>, <b>#S</b>, or <b>card(S)</b> are all acceptable for the cardinality of a set S</li> <li> <b>+-</b> (not +/- or ±)</li> <li> <b>0th</b>, <b>1st</b>, <b>2nd</b>, <b>3rd</b>, <b>4th</b>, ... (not 0-th, 1-st, 2-nd, 3-rd, 4-th, ...)</li> <li> <b>9-gon</b>, not nonagon: <b>10-gon</b>, not decagon; <b>11-gon</b> not hendecagon (a hendecagon is a 10-gon that lays eggs); etc. Numerals are used for polygons (and figurate numbers) with more than 8 sides</li> <li> <b>a(n)</b> for n-th term in sequence (not a[n] or a_n)</li> <li> a(n) denotes a single term in the sequence. To refer to the whole sequence, use any of <b>{a(n)}</b>, <b>[a(n)]</b>, or <b>(a(n))</b>. Of course curly brackets as in P = {2,3,5,7,11,...} usually refer to a set. When you need to distinguish between a sequence and the set of its terms, you need to spell out what you are doing in words. Say something like "Here [a(n): n >= 0] is the sequence, and {a(n)} is the set of its terms."</li> <li> approximately equal to: We don't have a special symbol, so say it in words: "Pi is approximately equal to 22/7".</li> <li> behavior (not behaviour - the OEIS uses US spelling)</li> <li> billion, trillion, ... (10^9, 10^12, ...) (American system, in which the prefix stands for n in 10^(3+3n))</li> <li> binomial(n,k) or C(n,k) for binomial coefficients; the former is preferred but the latter is acceptable in formulas if there are quite a few coefficients. Capitalize "Binomial" only at the beginning of sentence</li> <li> cancellation (not cancelation) is the correct spelling</li> <li> ceiling (not ceil; not Ceiling, unless at the beginning of a sentence)</li> <li> color (not colour - the OEIS uses US spelling)</li> <li> cos(x) (not Cos[x]) </li> <li> cubefree (not cube-free, not cube free)</li> <li> dependent (not dependant)</li> <li> dissectible (not dissectable)</li> <li> e for 2.718281828459... (not E)</li> <li> exponentiation: use ^ rather than **, ², or ³.</li> <li> Fibonacci (not fibonacci)</li> <li> floor (not Floor, unless at the beginning of a sentence). Floor(x) is often denoted by [x].</li> <li> Gamma (not GAMMA), for the Gamma function.</li> <li> GCD (not g.c.d. or G.C.D.; not hcf or h.c.f. or HCF or H.C.F.): we prefer either GCD or gcd.</li> <li> generalize (not generalise - the OEIS uses US spelling)</li> <li> groups: The OEIS uses the modern names for groups, as in the ATLAS of Finite Groups and the International Tables for Crystallography. In particular, the dihedral group of order 2n is denoted by D_{2n}. (The old name was D_n.)</li> <li> HCF, see GCD</li> <li> i, not I, for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {-1}}}</annotation> </semantics> </math></span><img src="https://en.wikipedia.org/api/rest_v1/media/math/render/svg/4ea1ea9ac61e6e1e84ac39130f78143c18865719" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.906ex; height:3.009ex;" alt="{\displaystyle {\sqrt {-1}}}" /></span>, the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a>. You can always add 'where i is the imaginary unit' to ensure nobody mistakes it for a summation index.</li> <li> iff is a perfectly acceptable abbreviation for "if and only if"</li> <li> Im, not im, for imaginary part of a complex number</li> <li> independent (not independant)</li> <li> infinity (not Inf, inf), but oo is allowed, especially in formulas</li> <li> Integral_{x=1..2} f(x) dx or Integral_{x=0..oo} f(x) dx</li> <li> The Iverson bracket is very useful in formulas: if P is some property or condition, [P] = 1 if P is true, [P] = 0 if P is false. So you can say "+ 6*[n == 0 (mod 3)] where [] is the Iverson bracket" as a shorthand for "except you have to add 6 if n is a multiple of 3".</li> <li> J. S. Bach (not J.S. Bach - a period should be followed by a space, except in hyphenated names like J.-P. Serre)</li> <li> l (el): try to avoid l in formulas, in many fonts it looks exactly like 1 (one) or I (capital i). Use k or m instead.</li> <li> labeled, labeling (not labelled, labelling - the OEIS uses US spelling)</li> <li> LCM (not l.c.m. or L.C.M.): we prefer either LCM or lcm.</li> <li> lim_{n->P} for limit (use Limit_{n->P} at start of a sentence)</li> <li> log_2(x) for logs to base 2</li> <li> log(n) (not ln(x) or Log[x]) for logs to base e </li> <li> log_10(x) for logs to base 10</li> <li> < (not lrth)</li> <li> <= (not \le or \leq)</li> <li> mod (not %)</li> <li> multiplication sign: use * rather than X, ·, a period (dot), or ×. Both 6n^2+17n+1 and 6*n^2+17*n+1 are acceptable. </li> <li> n X n (not n x n, not nXn, not n by n, not n-by-n) </li> <li> n-th, m-th, i-th, j-th, etc. (not nth, mth, ith, jth)</li> <li> neighbor (not neighbour - the OEIS uses US spelling)</li> <li> nilpotent (not nil-potent)</li> <li> noncomposite (not non-composite)</li> <li> nondecreasing (not non-decreasing)</li> <li> nonempty (not non-empty)</li> <li> nonincreasing (not non-increasing)</li> <li> nonnegative (not non-negative)</li> <li> nonpositive (not non-positive)</li> <li> nonprime (not non-prime)</li> <li> nonsquare (not non-square)</li> <li> nonsquarefree (not non-squarefree)</li> <li> nontrivial (not non-trivial)</li> <li> nonunit (not non-unit)</li> <li> nonzero (not non-zero)</li> <li> occurring (not occuring or ocurring)</li> <li> octagon, not 8-gon: prefixes are used for figurate numbers below 9</li> <li> p(n) should be <b>prime(</b><i>n</i><b>)</b> <a href="https://oeis.org/A000040">A000040</a>, <b>partition(</b><i>n</i><b>)</b> <a href="https://oeis.org/A000041">A000041</a>, or something unrelated </li> <li> <b>partition(</b><i>n</i><b>)</b> is <a href="https://oeis.org/A000041">A000041</a>(n), and better than p(n) </li> <li> Phi(n,x) for cyclotomic polynomials</li> <li> phi for the golden ratio (sometimes tau), phi(n) for the Euler totient function <a href="https://oeis.org/A000010">A000010</a></li> <li> Pi for 3.141592653... (not pi)</li> <li> <b>prime(</b><i>n</i><b>)</b> is the n-th prime <a href="https://oeis.org/A000040">A000040</a>(n), and better than p(n) </li> <li> prime(n) (preferred), or p(n), is usually the n-th prime, but both prime(n) and p(n) are also used in other ways</li> <li> prime-indexed prime (not prime-index prime)</li> <li> <b>Product_{</b><i>k=a..b</i><b>}</b> for product notation (always use capital "P"), e.g., <kbd>Product_{k=1..n} a(k)</kbd></li> <li> proved (not proven)</li> <li> Re, not re, for the real part of a complex number</li> <li> recurrence (not recurence or reccurrence)</li> <li> recurring (not recuring or reccurring)</li> <li> semiprime (not semi-prime)</li> <li> sin(x) (not Sin[x]) </li> <li> spaces: follow the end of a sentence with one space or two, either way is acceptable</li> <li> sqrt(x) (not Sqrt[x] or √x)</li> <li> squarefree (not square-free)</li> <li> submatrix (not sub-matrix)</li> <li> <b>Sum_{</b><i>k=a..b</i><b>}</b> for summation notation (always use capital "S"), e.g., <kbd>Sum_{n>0} a(n)</kbd></li> <li> Sum_{i=1..n} Sum_{j=1..i} f(i,j,n) for a double sum</li> <li> tetranacci (not Tetranacci)</li> <li> triangular (not Triangular, unless at the beginning of a sentence)</li> <li> tribonacci (not Tribonacci)</li> <li> zeroth (not zeroeth)</li> <li> zeros (not zeroes)</li> <li> zeta (for lower case zeta, as in Riemann zeta function): use zeta not Zeta</li></ul> <h3><span class="mw-headline" id="Non-ASCII_characters">Non-ASCII characters</span></h3> <p>Don't use non-ASCII characters in mathematical text! The standard style in the OEIS is to use ASCII representations of mathematical symbols, not Unicode. For example write <= and >= not ≤ and ≥, do not use the Unicode ellipsis …, do not use Greek letters (π, Σ) and so on. </p><p>The exception is for titles of published works and names of authors, OEIS contributors, places, institutions, etc. whose proper spelling requires non-ASCII characters. For example these are fine: </p> <ul><li> "Geneviève Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004." </li> <li> <a href="https://oeis.org/A033308">A033308</a> Decimal expansion of Copeland-Erdős constant: concatenate primes. (Links section: Mikołaj Morzy, Tomasz Kajdanowicz, Przemysław Kazienko, ...)</li></ul> <h3><span class="mw-headline" id="Grammar">Grammar</span></h3> <p>The possessive of a singular noun is formed by adding an apostrophe and an S, even if the noun ends in S. Write "Lucas's theorem", not "Lucas' theorem" (or perhaps "the Lucas theorem"). This rule is not universally accepted, so when directly quoting material for which the original editor did not abide by it, the quotation should not be altered. </p> <h2><span class="mw-headline" id="Common_mistakes_in_English">Common mistakes in English</span></h2> <ul><li> Using a(n) to refer to the whole sequence. That's wrong, a(n) is the n-th term. <ul><li> To refer to the full sequence, use {a(n)} or the A-number, such as <a href="https://oeis.org/A123456">A123456</a>.</li></ul></li></ul> <ul><li> "allows to" should be changed to "allows us to" or "allows one to"</li></ul> <ul><li> "amount" (referring to a number) should be "number" <ul><li> WRONG: "The amount of primes in ..."</li> <li> CORRECT: "The number of primes in ..." </li> <li> CORRECT: "The amount of butter in the cake ..."</li> <li> WRONG: "The amount of eggs in the cake ..."</li> <li> CORRECT: "The number of eggs in the cake ..."</li></ul></li></ul> <ul><li> "be integer" is wrong. <ul><li> WRONG: "Let k be integer"</li> <li> CORRECT: "Let k be an integer"</li></ul></li></ul> <ul><li> "couples" instead of "pairs" <ul><li> WRONG: "a(n) is the number of couples of binary matrices..."</li> <li> CORRECT: "a(n) is the number of pairs of binary matrices..."</li></ul></li></ul> <ul><li> "counts the number of" is wrong. Unless you are working in a hardware store, you don't count numbers. <ul><li> WRONG: "a(n) counts the number of ..."</li> <li> CORRECT: "a(n) is the number of ..."</li> <li> CORRECT: "a(n) gives the number of ..."</li></ul></li></ul> <ul><li> "Except a(5) = 91, ..." is wrong <ul><li> WRONG: "Except a(5) = 91, all terms are ..."</li> <li> CORRECT: "Except for a(5) = 91, all terms are ..."</li> <li> WRONG: "Except the number 2 ..."</li> <li> CORRECT: "Except for the number 2 ..."</li></ul></li></ul> <ul><li> "fulfills" is almost always wrong: the correct English word is "satisfies". For some reason, this error is very common among French and German speakers.</li></ul> <ul><li> "greater or equal" is wrong <ul><li> WRONG: "greater or equal to n"</li> <li> WRONG: "greater or equal n"</li> <li> CORRECT: "greater than or equal to n"</li> <li> CORRECT: ">= n"</li></ul></li></ul> <ul><li> "its" versus "it's": <ul><li> "Its", no apostrophe, is the possessive of the pronoun "it":   "the sequence is new, and its author is J. Smith"</li> <li> "It's", with an apostrophe, is short for "it is" or "it has":   "the sequence is new, but it's wrong"</li></ul></li></ul> <ul><li> "less or equal" is wrong <ul><li> WRONG: "less or equal to n"</li> <li> WRONG: "less or equal n"</li> <li> CORRECT: "less than or equal to n"</li> <li> CORRECT: "<= n"</li></ul></li></ul> <ul><li> "respectfully" when you should have said "respectively": <ul><li> WRONG: "The terms congruent to 0, 1, 2 (mod 3) are respectfully given by <a href="https://oeis.org/A000001">A000001</a>, <a href="https://oeis.org/A000002">A000002</a>, <a href="https://oeis.org/A000003">A000003</a>"</li> <li> CORRECT: "The terms congruent to 0, 1, 2 (mod 3) are respectively given by <a href="https://oeis.org/A000001">A000001</a>, <a href="https://oeis.org/A000002">A000002</a>, <a href="https://oeis.org/A000003">A000003</a>"</li> <li> CORRECT: "The terms congruent to 0, 1, 2 (mod 3) are given by <a href="https://oeis.org/A000001">A000001</a>, <a href="https://oeis.org/A000002">A000002</a>, <a href="https://oeis.org/A000003">A000003</a>, respectively"</li></ul></li></ul> <ul><li> "triplets" when you should have said "triples" <ul><li> WRONG: "a(n) is the number of triplets of binary matrices..."</li> <li> CORRECT: "a(n) is the number of triples of binary matrices..."</li> <li> Similarly, "quadruple" is preferred over "quadruplet", and so on.</li></ul></li></ul> <ul><li> "unique" when you should have said "distinct" <ul><li> WRONG: The list "Tom, Tom, Mary, John" contains three unique names" </li> <li> CORRECT: The list "Tom, Tom, Mary, John" contains three distinct names"</li></ul></li></ul> <h2><span class="mw-headline" id="Technical_definitions">Technical definitions</span></h2> <ul><li> Divisors - often a source of confusion! <ul><li> divisors: numbers d in the range 1 <= d <= n which divide n (<a href="https://oeis.org/A000005">A000005</a>, <a href="https://oeis.org/A000203">A000203</a>) </li> <li> aliquot divisors, aliquot parts: numbers d < n which divide n (see <a href="https://oeis.org/A032741">A032741</a>, <a href="https://oeis.org/A001065">A001065</a>)</li> <li> proper divisors, nontrivial divisors: officially these terms refer to divisors d of n with 1 < d < n (<a href="https://oeis.org/A070824">A070824</a>), but are often used incorrectly for divisors d of n with 1 <= d < n (<a href="https://oeis.org/A032741">A032741</a>, <a href="https://oeis.org/A001065">A001065</a>). You should always specify which definition you are using.</li> <li> prime divisors vs. divisors: a common mistake is to say "divisor" when you mean "prime divisor" or even "prime factor".<br /> (Prime <i>factors</i> may occur with multiplicity, while <i>divisors</i> may include <i>p</i>, <i>p</i>^2, ... but not the same <i>p</i> twice: <i>prime divisors</i> is a synonym for <i>prime factors without repetition</i>.) </li> <li> omega(n) and Omega(n): omega(n) is the number of distinct primes dividing n (<a href="https://oeis.org/A001221">A001221</a>), whereas Omega(n) or bigomega(n) counts them with multiplicity (<a href="https://oeis.org/A001222">A001222</a>)</li></ul></li></ul> <ul><li> What does "mod n" mean? Many contributors to the OEIS find this confusing. <ul><li> a == b (mod c) means that a-b is a multiple of c (one reads this as "a is congruent to b mod c"). So 12 == 8 (mod 2).</li> <li> a mod c = b means that the remainder when a is divided by c is b. So 12 mod 2 is 0.</li></ul></li></ul> <h2><span class="mw-headline" id="Sequences_with_conjectured_terms">Sequences with conjectured terms</span></h2> <p>In principle, the terms shown in an OEIS entry should have been proved to be correct and complete as far as they are shown. For example, in the list of Mersenne primes, <a href="https://oeis.org/A000043">A000043</a>, we don't include terms which are known to be in the sequence if it is possible that there are earlier terms which have not yet been found (although such terms are mentioned in the Comments or Extensions sections). </p><p>What do we do when there are terms in a sequence which are only conjectural? </p> <ul><li> The most common situation occurs when we know a certain number of terms, but we have only conjectures for the next few terms. In this case we give the terms that are certain in the Data section and the conjectured terms in the Comments or Extensions. This is the rule that we use to handle most cases. Example: <a href="https://oeis.org/A000952">A000952</a>, numbers n == 2 (mod 4) for which a conference matrix of order n exists. It is only a conjecture that the next term is 66.</li> <li> More than enough terms are known to fill three lines in the Data section, but there are gaps further along in the sequence. In this case we give the known terms (up to the first gap) in a <a href="/wiki/B-files" title="B-files">b-file</a>, and all the terms - with gaps, question marks, or ranges for the uncertain terms - in an a-file. Example: <a href="https://oeis.org/A072942">A072942</a>, which has both a b-file and an a-file. <a href="https://oeis.org/A046057">A046057</a> is a sequence from group theory which has an a-file although we don't know enough terms for certain to give a b-file.</li> <li> We only know a few terms for certain, but there is a conjectured generating function (which may or may not be correct). In this case we sometimes give two sequences, one for the known values and one for the sequence produced by the generating function. Example: <a href="https://oeis.org/A008368">A008368</a>, arising from the face-centered cubic lattice, and <a href="https://oeis.org/A023054">A023054</a>, from the proposed generating function.</li> <li> An extreme example is the sequence of Riesel numbers, <a href="https://oeis.org/A076337">A076337</a>, in which only the first term (509203) is known for certain. This violates all our rules, but is included in the OEIS because it is an important problem in number theory, and in the hope that having an entry for it in the OEIS will one day lead to the computation of further terms. The most likely extension is given by <a href="https://oeis.org/A101036">A101036</a>. We hope that one day it will be possible to merge the two entries.</li> <li> Two further extreme examples: If we were to insist on giving only terms which are known for certain, neither sequence would exist. Because of the importance of these problems, we have made exceptions and relaxed the rules. <ul><li> The Brier numbers, <a href="https://oeis.org/A076335">A076335</a>. Seven terms are known, but it is only a conjecture that they are the first seven terms. Even the first term shown is only conjectured to be the smallest.</li> <li> The minimal number of polygonal pieces needed for dissecting a regular polygon with n sides into an equilateral triangle of the same area: <a href="https://oeis.org/A110000">A110000</a>. This is a lovely problem, but only the trivial term a(3)=1 is known for certain. The other terms listed are just upper bounds. Again we hope that including this sequence in the OEIS will lead to the computation of further terms. </li></ul></li> <li> <a href="https://oeis.org/A000373">A000373</a> is a different kind of example. Here there is an explicit formula for a(n), and we can compute as many terms as we wish, but at the time of writing, it was only a conjecture that this was the answer to a question of Yuri Manin about Moufang loops (in fact, later the conjecture turned out to be false).</li> <li> <a href="/wiki/Probable_primes" title="Probable primes">Probable primes</a>. We take the point of view that the numbers which at present are known only to be probable primes will eventually be shown to be primes, so we don't regard sequences involving such numbers as conjectural. For example, see <a href="https://oeis.org/A004061">A004061</a>, numbers n such that (5^n-1)/4 is prime. Whenever possible, you should nonetheless mention which terms only correspond to probable primes.</li> <li> See also the entry in the Index to the OEIS for <a href="/wiki/Index_to_OEIS:_Section_Con#conjectures" title="Index to OEIS: Section Con">conjectured sequences</a>.</li></ul> <h2><span class="mw-headline" id="If_you_have_solved_a_famous_open_problem">If you have solved a famous open problem</span></h2> <p>such as Goldbach's conjecture, the 3x+1 conjecture, etc., the OEIS is not the place to publish it. First publish your proof in a (reputable) mathematics journal. </p> <h2><span class="mw-headline" id="See_also">See also</span></h2> <ul><li> <a href="/wiki/Style_Sheet_for_OEIS_Wiki" title="Style Sheet for OEIS Wiki">Style Sheet for OEIS Wiki</a></li></ul> <table class="wikitable" cellspacing="0" cellpadding="4px" style="margin: 1em auto; border-collapse: collapse; border: 1px solid darkgray; background: #f3fff3; color: black; empty-cells: show; text-align: center;"> <caption> OEIS sequence entry fields </caption> <tr> <td> <span class="smallcaps" style="font-variant: small-caps;">Name</span> · <span class="smallcaps" style="font-variant: small-caps;">Data</span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Offsets" title="Offsets">Offset</a></span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Comments" title="Comments">Comments</a></span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/References" title="References">References</a></span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Links" title="Links">Links</a></span> · <span class="smallcaps" style="font-variant: small-caps;">Formula</span> · <span class="smallcaps" style="font-variant: small-caps;">Example</span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Maple" title="Maple">Maple</a></span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a></span> · <span class="smallcaps" style="font-variant: small-caps;">Prog</span> · <span class="smallcaps" style="font-variant: small-caps;">Crossrefs</span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Keywords" title="Keywords">Keyword</a></span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Author" title="Author">Author</a></span> · <span class="smallcaps" style="font-variant: small-caps;"><a href="/wiki/Extensions" title="Extensions">Extensions</a></span> </td></tr></table>   </div>  </div><div class="printfooter"> Retrieved from "<a dir="ltr" href="https://oeis.org/w/index.php?title=Style_Sheet&oldid=1662953">https://oeis.org/w/index.php?title=Style_Sheet&oldid=1662953</a>"</div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Categories</a>: <ul><li><a href="/wiki/Category:Style_sheets" title="Category:Style sheets">Style sheets</a></li><li><a href="/wiki/Category:OEIS_Contribution" title="Category:OEIS Contribution">OEIS Contribution</a></li></ul></div></div>  <div class="visualClear"></div> </div> </div> </div> <div id="column-one"> <h2>Navigation menu</h2> <div id="p-cactions" class="portlet" role="navigation"> <h3>Views</h3> <div class="pBody"> <ul> <li id="ca-nstab-main" class="selected"><a href="/wiki/Style_Sheet" title="View the content page [c]" accesskey="c">Page</a></li> <li id="ca-talk"><a href="/wiki/Talk:Style_Sheet" rel="discussion" title="Discussion about the content page [t]" accesskey="t">Discussion</a></li> <li id="ca-viewsource"><a href="/w/index.php?title=Style_Sheet&action=edit" title="This page is protected.
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