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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>FAQ for OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/FAQ.html" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fFAQ.html">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="FAQ for OEIS"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <a href="/hints.html">Hints</a> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <center> <h1>FAQ for the <a href="Seis.html">On-Line Encyclopedia of Integer Sequences</a></h1> </center> <center> <h2>Frequently Asked Questions</h2> </center> Last updated Jun 07 2008. I need to update this page to refer to the new OEIS at oeis.org - N. J. A. Sloane, Jan 15 2011. <h3>Contents</h3> <h4>Use</h4> <a href="FAQ.html#Z03">Q:</a> What is the purpose of the OEIS? <a href="FAQ.html#Z01">Q:</a> How do I cite the OEIS in a paper? <a href="FAQ.html#Z02">Q:</a> Can you give some examples of successful applications of the OEIS? <a href="FAQ.html#Z001">Q:</a> Some advice for new users and new contributors? <a href="FAQ.html#Z002">Q:</a> OEIS Summer Rules, Jun 02 2008, but still valid today! <h4>Searching</h4> <a href="FAQ.html#Z17">Q:</a> How many terms do I need to look up a sequence? <a href="FAQ.html#Z17a">Q:</a> How do I find which sequences cross-reference a particular sequence? <a href="FAQ.html#Z18">Q:</a> I looked up a really basic sequence (the number of abelian groups of order n, in fact), and I was surprised to find that it wasn't there. How come? <a href="FAQ.html#Z19">Q:</a> I've heard about the Motzkin numbers, but I don't know the beginning of the sequence, so how can I find them? <a href="FAQ.html#Z20">Q:</a> I was trying to find the entry for the Fibonacci numbers, but when I entered 2, 3, 5, 8, 13 I got too many matching sequences. <a href="FAQ.html#Z32">Q:</a> How do I find all the sequences that mention my name? <a href="FAQ.html#Z38">Q:</a> How can I get hold of all the sequences submitted by John Smith that mention "lattice", so I can analyze them on my computer? <h4>Semantics</h4> <a href="FAQ.html#Z16">Q:</a> Sometimes a sequence will say "n^2 + 1 is prime", sometimes it says "Primes of the form n^2 + 1". What's the difference? <a href="FAQ.html#Z21">Q:</a> Where can I find an explanation of all the different keywords, like "core" and "nice"? <a href="FAQ.html#Z23">Q:</a> What does the "offset" mean? <a href="FAQ.html#Z42">Q:</a> What does the keyword "more" mean? <a href="FAQ.html#Z26">Q:</a> What does the keyword "base" mean? <a href="FAQ.html#Z25">Q:</a> Can you give an example of a "dumb" sequence? <a href="FAQ.html#Z41">Q:</a> Why are there sequences with keyword "dead"? <h4>Submissions</h4> <a href="FAQ.html#Z04">Q:</a> Which sequences should I submit to the OEIS? <a href="FAQ.html#Z05">Q:</a> If I just make up a definition of a sequence, should I submit it? <a href="FAQ.html#Z07">Q:</a> What should I do before submitting a new sequence? <a href="FAQ.html#Z06">Q:</a> How long should I spend on a submission to the OEIS? <a href="FAQ.html#Z07a">Q:</a> What "Subject" line should I use when submitting a new sequence or comment? <a href="FAQ.html#Z34">Q:</a> I am sending in a comment on one of the sequences. Should I send a copy to the <a href="http://www.seqfan.eu/">SeqFan mailing list</a>? <a href="FAQ.html#Z12">Q:</a> What kinds of number may appear in a sequence? Can a sequence include numbers that begin with 0? <a href="FAQ.html#Z43">Q:</a> A comma appeared in the middle of a number in my sequence - why? <a href="FAQ.html#Z37">Q:</a> Should one specify links to the <a href="Sindx.html">Index</a> when submitting sequences? <a href="FAQ.html#Z24">Q:</a> What are some of the reasons why sequences are rejected? <a href="FAQ.html#Z35">Q:</a> How can I find out if the sequence I submitted was accepted or rejected? <h4>Notation</h4> <a href="FAQ.html#Z08">Q:</a> What notation should I use in equations in the comment and formula lines? <a href="FAQ.html#Z09">Q:</a> Is it OK to use LaTex notation in equations? <a href="FAQ.html#Z10">Q:</a> Should I use juxtaposition to denote multiplication, or should I put a "*" or "." between the things being multiplied? <a href="FAQ.html#Z11">Q:</a> How should I indicate summations? <a href="FAQ.html#Z15">Q:</a> Should I denote infinity by "oo"? <a href="FAQ.html#Z39">Q:</a> What does "lgdegf" mean in a reply from Superseeker? <h4>Format</h4> <a href="FAQ.html#Z30">Q:</a> What is the best format to use when sending in more terms for an existing sequence? <a href="FAQ.html#Z22">Q:</a> Where can I find an explanation of the internal format used in the database? The %I, %S, etc. lines? <a href="FAQ.html#Z07b">Q:</a> I notice that sometimes you give more than three lines of terms for a sequence. What's the story? <a href="FAQ.html#Z13">Q:</a> What's the preferred way to enumerate array elements to get an OEIS sequence? <a href="FAQ.html#Z14">Q:</a> How should an array or triangle be included with the submission? <a href="FAQ.html#Z31">Q:</a> Some of the entries have figures or other files associated with them. What's your policy on this? <a href="FAQ.html#Z40">Q:</a> Questions concerning decimal expansion of constants. <h4>Participation</h4> <a href="FAQ.html#Z27">Q:</a> How many new sequences and comments come in each day? How big is the database? <a href="FAQ.html#Z27a">Q:</a> What can I do to help? <a href="FAQ.html#Z44">Q:</a> You asked people to help edit sequences with keyword "uned". What exactly do you need done? <a href="FAQ.html#Z45">Q:</a> I am emailing you a corrected version of a sequence. Should I say "Edited by ...", "Extended by ...", or not sign it at all? <a href="FAQ.html#Z46">Q:</a> How can one obtain a file of all the sequences (stripped of formatting) for running tests? <a href="FAQ.html#Z33">Q:</a> Why are there no mirror sites? <a href="FAQ.html#Z28">Q:</a> Can one subscribe to the comment mail queue? There is already a lot of information about the Encyclopedia on other pages, and some of these answers will just be pointers to the appropriate page. <hr> <center> <h2>Use</h2> </center> <hr> <a NAME="Z03">Q:</a> What is the purpose of the OEIS? A: The main purpose is to allow mathematicians or other scientists to find out if some sequence that turns up in their research has ever been seen before. If it has, they may find that the problem they're working on has already been solved, or partially solved, by someone else. Or they may find that the sequence showed up in some other situation, which may show them an unexpected relationship between their problem and something else. Another purpose is to have an easily accessible database of important, but difficult to compute, sequences. For example, if you're testing some conjecture about Mersenne primes, you can look up the ones that are known (see <a href="A000043">A000043</a>), rather than spending years recomputing them. For more information on this point, see the <a href="demo1.html">Demo</a> files and the <a href="Seis.html">Welcome</a> page. <hr> <a NAME="Z01">Q:</a> How do I cite the OEIS in a paper? A: Click <a href="Seis.html#reference">here</a>. That is a link to a section of the <a href="Seis.html">Welcome</a> page, which has a lot more information about the database. <hr> <a NAME="Z02">Q:</a> Can you give some examples of successful applications of the OEIS? A: See the <a href="cite.html">list of papers that have acknowledged help from the database</a>; also the <a href="demolast.html">comments from readers</a> on the last page of the <a href="demo1.html">Demo</a> files. <hr> <a NAME="Z001">Q:</a> Some advice for new users and new contributors? A: (From Jonathan Post (jvospost3(AT)gmail.com), Jun 07 2008) New OEIS contributors should be strongly encouraged to use the OEIS webcam to see the breadth and variety of those seqs deemed "nice." It is the equivalent of listening to a radio station that plays the greatest classical or jazz or rock songs (and for that auditory matter using the "listen" feature), or walking through a museum of unusually beautiful Mathematics (and, for that visual matter, encouraging the use of the "graph" feature). Another positive message to new OEIS contributors, to enhance that sense of community, and to provide a balance against "making stuff up" without reference to what is known and had been judged interesting, is, beyond looking for duplicates, looking from triples and n-tuples of sequences that are implicitly related, and making that relationship explicit, perhaps by showing that these are different rows or columns or diagonals of the same previously unshown array. Or by making the analogy: sequence A is to sequence B as sequence C is to sequence D. Or by using the transforms available on some sequence previously not so transformed. The goal is, not to merely reward ("nice") or punish ("less" or "probation" or silent deletion) those contributors externally, but by enhancing their intrinsic motivation to make a contribution more likely to be appreciated. <hr> <a NAME="Z002">Q:</a> OEIS Summer Rules, Jun 02 2008, but still valid today! A: <ul> <li> Do send important new sequences and comments, especially sequences that are in publications or web sites </li> <li> Don't send sequences that you made up, just because they are not in the OEIS </li> <li> - Submissions that seem arbitrary will be silently deleted </li> <li> Extensions of existing sequences are welcomed, also b-files, also corrections of bad errors. </li> </ul> Thank you! Neil Sloane <hr> <center> <h2>Searching</h2> </center> <hr> <a NAME="Z17">Q:</a> How many terms do I need to look up a sequence? A: It depends! Usually you should enter about 6 terms, starting with the second term. Leave off the first term or two, because people may disagree about where the sequence begins. Don't enter too many terms, because you may have more terms than are in the OEIS right now! But one regular user says: <blockquote> Don't hesitate to try the OEIS even if you only have a few terms. For example, the two terms 2, 1729 identify the "taxicab numbers" <a href="A011541">A011541</a>. For a better example, the single number 15170835645 identifies uniquely <a href="A003825">A003825</a>. </blockquote> For more information about looking up sequences, see the <a href="hints.html">hints file</a>. <hr> <a NAME="Z17a">Q:</a> How do I find which sequences cross-reference a particular sequence? A: Look up the A-number as a word (rather than as a sequence number). For example, to find all the sequences that mention the Narayana-Zidek-Capell numbers <a href="A002083">A002083</a>, enter     A002083     into the search window. If you only want to see sequence A002083, enter     id:A002083    . You could also enter     Narayana   Zidek     into the search window. For more information about looking up sequences, see the <a href="hints.html">hints file</a>. <hr> <a NAME="Z18">Q:</a> I looked up a really basic sequence (the number of abelian groups of order n, in fact), and I was surprised to find that it wasn't there. How come? A: You probably miscalculated one of the terms! It is there: <a href="A000688">A000688</a>. After 35 years most of the basic sequences are in the database now. When this happens, please recheck your calculations before submitting the sequence. It is also possible that you have included an initial term that most people don't include (perhaps starting a number-theoretic sequence at n=0 rather than n=1). Of course it is entirely possible that your sequence really isn't in the database, in which case please <a href="Submit.html">submit</a> it! <hr> <a NAME="Z19">Q:</a> I've heard about the Motzkin numbers, but I don't know the beginning of the sequence, so how can I find them? A: (1) Enter     Motzkin numbers     into the <a href="index.html">lookup page</a>. Or (2) use the <a href="Sindx.html">Index</a> to the OEIS. Incidentally, the Motzkin numbers are <a href="A001006">A001006</a>. <hr> <a NAME="Z20">Q:</a> I was trying to find the entry for the Fibonacci numbers, but when I entered 2, 3, 5, 8, 13 I got too many matching sequences. A: (January 2006: this problem should now be fixed. The following is the old answer to this question, which is still helpful.) Use the <a href="Sindx.html">Index</a> to the OEIS. If you are in the right ballpark, the replies will be sorted with the "core" sequences first, followed by the "nice" sequences, and your sequence should be the first one that is listed. But for common beginnings, like 2, 3, 5, 7 or 2, 3, 5, 8 there are a lot of possible continuations, and you should give more terms if you have them. Otherwise, try the <a href="Sindx.html">Index</a>. Or go to the <a href="Seis.html">Welcome</a> page, and download the section of the database containing sequences around the one you are interested in (in the lexicographic order), and then you can browse. But beware, those files are all quite large. Incidentally, the Fibonacci numbers are <a href="A000045">A000045</a>. <hr> <a NAME="Z32">Q:</a> How do I find all the sequences that mention my name? A: Enter your name in the search page. To find just those where your name is on the Author line, enter     author:Smith     for example. To find just those where your name is on the Extension line, enter     extension:Smith     for example. <hr> <a NAME="Z38">Q:</a> How can I get hold of all the sequences submitted by John Smith that mention "lattice", so I can analyze them on my computer? A: Simply enter     author:Smith   lattice     in the search page. <hr> <center> <h2>Semantics</h2> </center> <hr> <a NAME="Z16">Q:</a> Sometimes a sequence will say "n^2 + 1 is prime", sometimes it says "Primes of the form n^2 + 1". What's the difference? A: A description like "n^2 + 1 is prime" means that the sequence gives a list of the values of n such that n^2 + 1 is prime, that is, 1, 2, 4, 6, 10, 14, ... (<a href="A005574">A005574</a>). On the other hand, "Primes of the form n^2 + 1" means that the sequence gives a list of the actual primes, 2, 5, 17, 37, 101, 197, 257, ... (<a href="A002496">A002496</a>). It is easy to get them confused! (But in this case it is easy to tell the difference: 4 is not a prime.) <hr> <a NAME="Z21">Q:</a> Where can I find an explanation of all the different keywords, like "core" and "nice"? A: In the page that describes the <a href="eishelp2.html">format</a> used in replies from the database. Note that the keywords "huge" and "done" are no longer used. <hr> <a NAME="Z23">Q:</a> What does the "offset" mean? A: It tells you the subscript of the first term in the sequence. Examples: <ul> <li>The Fibonacci numbers (<a href="A000045">A000045</a>) are traditionally denoted by F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, F(4) = 3, ... This sequence starts with F(0), so the offset is 0. </li> <li>The prime numbers (<a href="A000040">A000040</a>) are prime(1) = 2, prime(2) = 3, prime(3) = 5, ...; and the offset is 1. </li> <li> More generally, the convention in the OEIS is that the first entry in a list has index 1 (rather than 0) so the offset for a list is 1. </li> <li> <a href="A062361">A062361</a> gives the number of triangular regions in a regular n-gon when all the diagonals are drawn. This only makes sense for n >=3, so the offset is 3. </li> <li><a NAME="Z40bis">If</a> the sequence gives the decimal expansion of a constant, the offset is the number of digits before the decimal point. <ul> <li> For example, the speed of light is 299792458 (m/sec), giving the sequence 2,9,9,7,9,2,4,5,8 (<a href="A003678">A003678</a>), with offset 9. </li> <li> The decimal expansion of Pi, 3.14159265358979..., gives the sequence 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,... (<a href="A000796">A000796</a>), with offset 1. </li> <li> For a number less than 1, the best thing is to give just the sequence of digits after the decimal point, so that the offset is 0. E.g. 1/sqrt(2) = 0.7071067811865475... gives the sequence 7,0,7,1,0,6,7,8,1,1,8,6,5,4,7,5,... (<a href="A020759">A020759</a>), with offset 0. </li> <li> The precise definition: if the sequence is a,b,c,d,... and the offset is t, then the number is .abcd... * 10^t. If the number is a.bcd... * 10^t where a is a single digit, then the sequence is a,b,c,d,... with offset t+1. </li> <li> If the constant is negative, say so, but give the decimal expansion of the absolute value. </li> <li> Always give the actual value in a %e line. For example %e A020759 1/sqrt(2) = 0.7071067811865475... And don't forget the keyword "cons". </li> <li> I found and corrected a huge number of wrong offsets for decimal expansions. Probably many more remain. That's why it is important to give the actual beginning of the decimal expansion in a %e line. </li> </ul> </li> </ul> In the internal format for a sequence the offset line (the %O line) contains two numbers.    The first is the offset as just defined.    The second gives the position of first entry greater than or equal to 2 in magnitude in the sequence (or 1 if no such entry exists), starting counting at 1. The second offset is used to determine the position of the sequence in the lexicographic order in the database. For further examples, see the "offset" section of the <a href="eishelp1.html#offset">internal format</a> page. <hr> <a NAME="Z42">Q:</a> What does the keyword "more" mean? A: This is a sequence where more terms are needed. Ideally the entry gives enough terms to fill three lines on your screen, like this: <pre> %S A027614 1,1,3,14,80,468,2268,10224,313632,9849600,21954240,8894136960, %T A027614 105857556480,20609598562560,650835095904000,80028503341516800, %U A027614 5018759207362252800,503681435808239001600,56090762228110443724800 </pre> or <pre> %S A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %T A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %U A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 </pre> If you can extend a sequence which has fewer terms than that, please do so, even if the keyword "more" is missing. See also <a href="FAQ.html#Z30"> What is the format to use when sending in more terms?</a> You can set the <a href="WebCam.html">WebCam</a> to browse the sequences that need extending, or use the <a href="index.html">main look-up page</a> to search for keyword:more. <hr> <a NAME="Z26">Q:</a> What does the keyword "base" mean? A: A sequence where the definition depends on which base we are using. Palindromes (numbers which are unchanged if the order of the digits is reversed, <a href="A002113">A002113</a>) are a classic example. <hr> <a NAME="Z25">Q:</a> Can you give an example of a "dumb" sequence? A: The number of pages in the n-th volume of the Harry Potter series of children's books. This was actually submitted! It was rejected for many reasons, one of which is that it is not well-defined (English edition or American? Hard-cover or paperback?). <hr> <a NAME="Z41">Q:</a> Why are there sequences with keyword "dead"? A: Usually they indicate a published sequence that was wrong. The point is that if someone sees the erroneous sequence in a book and looks it up in the OEIS, the entry will point them to the right sequence. <hr> <center> <h2>Submissions</h2> </center> <hr> <a NAME="Z04">Q:</a> Which sequences should I submit to the OEIS? A: Any that actually show up in your research. If you looked up a sequence in the OEIS and were disappointed that it wasn't there, you should probably <a href="Submit.html">submit</a> it so the next person who looks for it will find it. Also, most sequences that appear in published papers should be in the OEIS. That way, if someone sees a sequence in a paper and looks it up, they'll be able to find out if anything new has been learned about the sequence since the paper was published. Even if a published sequence happens to be wrong, it should be in the OEIS, with a cross-reference to the correct sequence. <hr> <a NAME="Z05">Q:</a> If I just make up a definition of a sequence, should I submit it? A: Probably not. It's very easy to define new sequences, but most of them are unlikely to be useful to anyone. There are exceptions. If it is a really beautiful sequence, go ahead and submit it! See the EKG sequence (<a href="A064413">A064413</a>) for an example of a made-up sequence of great interest. <hr> <a NAME="Z07">Q:</a> What should I do before submitting a new sequence? A: Check for connections with sequences already in the database. For example, plot the sequence (or its log) to check for clues that it could be formed by intertwining two known sequences. For triangles or tables, check the columns, row sums, skew diagonals etc. to see if they are already in the database. If so, mention this in the submission. Check your sequence with <a href="ol.html">Superseeker</a> Study the first differences of your sequence to see if they provide any clues. Make sure you give the correct offset (see <a href="FAQ.html#Z23">above</a>)! If there is a relation to a geometric or combinatorial problem, describe this: it's valuable information. And finally, if possible, please give a formula! <hr> <a NAME="Z06">Q:</a> How long should I spend on a submission to the OEIS? A: After you've computed enough terms to fill 3 lines, or as many terms as you can, you should probably spend at least an hour writing and checking the definition, comments, references, cross-references, etc. If you don't think the sequence is worth spending an hour of your time on, then it's probably not worth having in the OEIS. Take the time to make sure that everything is accurate and explained clearly, so that someone who hasn't seen the sequence before will understand how it's defined and why it's interesting or important. Include any references that you know about. Remember the advice given in the <a href="Submit.html">submit new sequence</a> page: <blockquote> IMPORTANT: Thousands of people use the sequence database every day. Please take great care that the terms you send are absolutely correct. The standards are those of a mathematics reference work. </blockquote> <hr> <a NAME="Z07a">Q:</a> What "Subject" line should I use when submitting a new sequence or comment? A: If you are sending these by email, rather than using the <a href="Submit.html">submit new sequence or comment</a> web page, please use: Subject: NEW SEQ     for unnumbered new sequences, Subject: PRE-NUMBERED     for pre-numbered new sequences, Subject: COMMENT     for comments on existing sequences, Subject: EDITED     for a sequence that you have completely edited. It makes the editing process easier if there is only one type of comment in a message. That is, please don't mix "Comments" and "New Sequences" (or "Edited Sequences") in a single email! <hr> <a NAME="Z34">Q:</a> I am sending in a comment on one of the sequences. Should I send a copy to the <a href="http://www.seqfan.eu/">SeqFan mailing list</a>? A: No, that's not necessary. <hr> <a NAME="Z12">Q:</a> What kinds of number may appear in a sequence? Can a sequence include numbers that begin with 0? A: No! (except for 0 itself) Numbers in sequences must be positive or negative integers (or 0). Acceptable numbers are   1,   5,   101,   0,   -25,   etc. Unacceptable numbers are:   020,   7.125,   0.725E03,   3/4,   22?,   123...6   6^6^6^6. But see also the section in the <a href="hints.html#fract">hints file</a> on dealing with fractions and real numbers. <hr> <a NAME="Z43">Q:</a> A comma appeared in the middle of a number in my sequence - why? A: Because you split a number across two lines! My formatting programs assume numbers in a submission are separated by commas, spaces or newlines. If you mouse a sequence into the window, the mouse may introduce newlines, like this: <pre> 8,12,20,24,32,36,48,52,60,68,80,84,96,100,112,120,128,140,144,152,168,172,19 2,200... </pre> That would cause the number 192 to appear as 19,2 <hr> <a NAME="Z37">Q:</a> Should one specify links to the <a href="Sindx.html">Index</a> when submitting sequences? A: You certainly may if you know what you are doing! There are plenty of examples in the database. Just include the link in a links window on the submission page. Here is a typical link, to the index entries dealing with the Goldbach conjecture. But when you type it, please type "greater than", "less than", and double-quotes as single characters. Don't type "less than" as "ampersand l t semicolon" as I had to to make this line visible! <a href="Sindx_Go.html#Goldbach">Index entries</a> for sequences related to Goldbach conjecture</a>. At some later time you should then send me a list of updates to the index itself. <hr> <a NAME="Z24">Q:</a> What are some of the reasons why sequences are rejected? A: Common reasons are: <ul> <li> sequence is an incorrect version of a sequence already in the database </li> <li> sequence is not well defined </li> <li> definition of sequence involves an arbitrary but large integer or an arbitrary real parameter </li> <li> sequence is too contrived or artificial </li> <li> sequence is too short </li> <li> sequence contains numbers involving decimal points, up-arrows, or other unacceptable characters (see <a href="FAQ.html#Z12">above</a>) </li> </ul> Example: primes that contain the digits 2003. The "2003" is an arbitrary and large parameter. Example: numbers n such that the digits of n appear in all powers n^s with s = 1 through 20: 0, 1, 5, 6, 10, 25, 50, 60, 76, 100, 101, ... The parameter 20 here is arbitrary. If we replaced it by 38, say, the sequence would change. Example: digits of n appear in n^2, n^3 and prime(n): 976, 5903, 10513, 68793, 94682, ... Too contrived! Example: even numbers that are not the sum of two primes: 2, ... Too short! Assuming the Goldbach conjecture is true, there are no more terms. On the other hand, there are several legitimate sequences based on the conjecture, e.g. <a href="A002372">A002372</a>. See also the <a href="Sindx_Go.html#Goldbach">Index entries</a> for sequences related to Goldbach conjecture</a>. Example: superfactorials, 1, 4, 6^6^6^6^6^6, 24^24^...^24 (with 24 copies of 24), ... - contains unacceptable numbers. On the other hand, number sequences that have actually appeared on quizzes or tests are welcomed. One of the reasons for the OEIS's existence is to help people with such tests! <hr> <a NAME="Z35">Q:</a> How can I find out if the sequence I submitted was accepted or rejected? A: <ul> <li> Wait a few days, then use the <a href="index.html">Lookup</a> page. </li> <li> Or, go to the <a href="Seis.html">Welcome</a> page, and scroll down to the "Recent additions" section. </li> </ul> <hr> <center> <h2>Notation</h2> </center> <hr> <a NAME="Z08">Q:</a> What notation should I use in equations in the comment and formula lines? A: Try to use notation that's as close to standard mathematical notation as is possible using ASCII text. Don't use notation that's specific to Maple, Mathematica, PARI, or some other computer language, except in %p, %t, or %o lines. In particular, the arguments of functions should be enclosed in parentheses, not brackets; most function names should not be capitalized. Here are some common examples: <center> <TABLE border="1" cellpadding="2" width="90%"> <tr><th width="20%" align="left">Use:</th><th align="left">to mean:</th></tr> <tr><td>binomial(n,k)</td><td>the binomial coefficient n-choose-k</td></tr> <tr><td>sigma(n)</td><td> the sum of the divisors of n, <a href="A000203">A000203</a>(n)</td></tr> <tr><td>phi(n)</td><td> the Euler phi (or totient) function of n, <a href="A000010">A000010</a>(n)</td></tr> <tr><td>mu(n)</td><td> the Moebius function of n, <a href="A008683">A008683</a>(n)</td></tr> <tr><td>pi(n)</td><td> the number of primes <= n, <a href="A000720">A000720</a>(n)</td></tr> <tr><td>prime(n)</td><td> the n-th prime, <a href="A000040">A000040</a>(n)</td></tr> <tr><td>omega(n)</td><td> the number of distinct prime divisors of n, <a href="A001221">A001221</a>(n)</td></tr> <tr><td>bigomega(n)</td><td>the number of prime divisors of n, with multiplicity, <a href="A001222">A001222</a>(n)</td></tr> <tr><td>sqrt(x)</td><td> the (positive) square root of x</td></tr> <tr><td>floor(x)</td><td> the largest integer <= x</td></tr> <tr><td>ceiling(x)</td><td> the smallest integer >= x</td></tr> <tr><td>round(x)</td><td> the integer closest to x.</td></tr> </TABLE> </center> In most cases, it's a good idea to explain what function you mean, since some of these function names aren't standardized, or are used for other things. For example, "pi(n+1)" might also mean the number pi multiplied by n+1. Use cross-references to other sequences to help with the explanations. <hr> <a NAME="Z09">Q:</a> Is it OK to use LaTex or Maple notation in equations? A: No, please don't! Use notation that can be understood by humans. Say     (1+x)/(1-x)     not     $\frac{(1+x)}{(1-x)}$. Say     n^2/2     not     1/2n^2. Say     A/(B*C*D)     not     A/B/C/D Say     sigma     not     $\sigma$. <hr> <a NAME="Z10">Q:</a> Should I use juxtaposition to denote multiplication, or should I put a "*" or "." between the things being multiplied? A: Either juxtaposition or an asterisk (*) are OK. Don't use a dot to denote multiplication. <hr> <a NAME="Z11">Q:</a> How should I indicate summations? A: There are many acceptable ways to do this. All of the following examples are OK. sum_{i=1..n} i^2 + i sum_i=1..n (i^2+i) sum_{d|n} d^3 sum_{ 2 <= p <= n, p prime} p^2 Other styles also acceptable, as long as they are clear! <hr> <a NAME="Z15">Q:</a> Should I denote infinity by "oo"? A: Generally it is better to say "infinity" explicitly. <hr> <a NAME="Z39">Q:</a> What does "lgdegf" mean in a reply from Superseeker? A: It stands for "logarithmic derivative", which is nothing more than the derivative of the log of a function: <PRE> d log(f(x)) f'(x) lgdegf f(x) = ----------- = ----- dx f(x) </PRE> The replies from Superseeker are sometimes hard to read, I admit! For example, suppose it says: <PRE> SUGGESTION: LISTTOALGEQ FOUND ONE OR MORE ALGEBRAIC EQUATIONS SATISFIED BY THE GEN. FN. WARNING: THESE MAY BE ONLY APPROXIMATIONS! Equation(s) and type(s) are: 2 3 [8 - 12 a(n) + 6 a(n) - a(n) , lgdegf] </PRE> What this means is the following. Let f(x) be the generating function for your sequence, and let a(x) be the logarithmic derivative of f(x). Then Superseeker has found that a(x) may satisfy the equation <PRE> 2 3 8 - 12 a(x) + 6 a(x) - a(x) = 0 </PRE> So you solve that for a(x), which is f'(x)/f(x), and then try to solve for f(x). Like I said, this takes a bit of getting used to! But it can be very helpful. <hr> <center> <h2>Format</h2> </center> <hr> <a NAME="Z30">Q:</a> What is the best format to use when sending in more terms for an existing sequence? A: Please put the full sequence (all the terms, not just the new ones) in the first window of the <a href="Submit.html">Contribute new seq. or comment</a> web page. In the "Comments" window, put something like "More terms". Or if you have found a mistake, say "Corrected and extended". If it is a signed sequence (that is, contains negative numbers), just give the signed version in the top window, and don't bother to include the sequence of absolute values. The updating programs will take care of that. <hr> <a NAME="Z22">Q:</a> Where can I find an explanation of the internal format used in the database? The %I, %S, etc. lines? A: See the <a href="eishelp1.html">internal format</a> page. <hr> <a NAME="Z07b">Q:</a> I notice that sometimes you give more than three lines of terms for a sequence. What's the story? A: There is no definite limit on the number of terms that are given in the database. The sequence of numbers of meanders (<a href="A005316">A005316</a>) for example, is exceptionally long. This is because the sequence is interesting, the terms are fairly difficult to compute, and so it seems worthwhile giving as many as possible. The editing programs will normally truncate the sequence to three lines (roughly 180 to 210 characters including the separating commas, depending on the program), but they can be overruled. If you feel the sequence is important enough to justify this, please add a note to that effect in the Comments. If fewer than three lines worth are given, feel free to compute some more terms! <hr> <a NAME="Z13">Q:</a> What's the preferred way to enumerate array elements to get an OEIS sequence? A: In the case of an infinite square array, <pre> a11 a12 a13 ... a21 a22 a23 ... a31 a32 a33 ... a41 a42 a43 ... ............... </pre> this normally gets read by antidiagonals and recorded as the sequence a11 a12 a21 a13 a22 a31 ... or a11 a21 a12 a31 a22 a13 ... (pick whichever seems nicer - or use both). See <a href="A003987">A003987</a> for an example. <hr> <a NAME="Z14">Q:</a> How should an array or triangle be included with the submission? A: Put it in the "Example" (or %e) lines. For instance (<a href="A079297">A079297</a>): <pre> %I A079297 %S A079297 1,2,6,3,9,15,4,12,20,28,5,15,25,35,45,6,18,30,42,54,66,7,21,35,49,63, %T A079297 77,91,8,24,40,56,72,88,104,120,9,27,45,63,81,99,117,135,153,10,30,50, %U A079297 70,90,110,130,150,170,190,11,33,55,77,99,121,143,165,187,209,231,12 %N A079297 Triangle read by rows: the k-th column is an arithmetic progression with difference 2k-1, and the top entry is the hexagonal number k*(2*k-1) (<a href="A000384">A000384</a>). %C A079297 The n-th row consists of the odd multiples of n from n*1 to n*(2n-1). %D A079297 R. Honsberger, Ingenuity in Math., Random House, 1970, p. 88. %F A079297 a(n,k) = n(2k-1) for 1<=k<=n. n-th row adds to n^3. %e A079297 Triangle begins: %e A079297 1 %e A079297 2 6 %e A079297 3 9 15 %e A079297 4 12 20 28 %e A079297 5 15 25 35 45 %e A079297 6 18 30 42 54 66 %K A079297 nonn,tabl,easy %O A079297 1,2 %A A079297 njas, Mar 04 2003 </pre> <hr> <a NAME="Z31">Q:</a> Some of the entries have figures or other files associated with them. What's your policy on this? A: As long as the files are not too big and serve a useful purpose they are welcomed. Examples of such files are: <ul> <li> a plain text file giving additional terms for an important sequence, when there are too many to fit on the %S, %T, %U lines (e.g. <a href="A000019">A000019</a>) </li> <li> a gif file illustrating the things being enumerated by the initial terms of a sequence (e.g. <a href="A003035">A003035</a>, <a href="A000012">A000012</a>) </li> <li> a plain text file giving a computer program for producing an important sequence, when this is too big to fit in the %p, %t or %o lines (e.g. <a href="A005132">A005132</a>) </li> <li> a postscript file plotting the initial terms of an important sequence, but only when this shows some unusual features (again see <a href="A005132">A005132</a>). In general such plots are unnecessary. </li> </ul> The reason for including these files on the OEIS web site is that it is hoped that this is more permanent than people's individual home pages. <hr> <a NAME="Z40">Q:</a> Questions concerning decimal expansion of constants. The OEIS contains many sequences giving the decimal expansions of important constants. For example, the decimal expansion of Pi, 3.14159265358979..., gives the sequence 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,... (<a href="A000796">A000796</a>), with offset 1. <ul> <li> Q: What does the "offset" mean for a constant? A: See <a href="FAQ.html#Z40bis">above</a>. </li> <li> Q: How do you handle negative numbers? A: If the constant is negative, say so, but give the decimal expansion of the absolute value. </li> <li> Reminder: Always give the actual value of the constant in a %e line. For example %e A020759 1/sqrt(2) = 0.7071067811865475... And don't forget the keyword "cons" (don't use "base"). </li> <li> Q: Do you also want the sequence formed by the continued fraction expansion of the constant? A: Yes! This should be a separate sequence, with keyword "cofr", and there should be cross-references (%Y lines) linking the two sequences. </li> </ul> <hr> <center> <h2>Participation</h2> </center> <hr> <a NAME="Z27">Q:</a> How many new sequences and comments come in each day? How big is the database? A: The number of new sequences arriving has remained fairly constant at about 10000 per year (i.e. 30 a day) for several years. The number of comments keeps increasing, and at present averages between 30 and 60 a day. Web traffic on all my web pages averages about 600000 page-downloads per month. The number of sequences in the OEIS is posted on the main <a href="index.html">Lookup</a> page and is constantly updated. As of January 2006 it is around 120000. The database (just the entries for the sequences, not the illustrations) occupies about 100 megabytes. <hr> <a NAME="Z27a">Q:</a> What can I do to help? A: <ul> <li> Look for sequences in papers in the <ul> <li> <a href="http://arXiv.org">LANL e-print archive</A> (in all categories, not just math.), </li> <li> <a href="http://www.combinatorics.org/">Electronic Journal of Combinatorics</a>, </li> <li> <a href="http://www.emis.de/journals/SLC/">Seminaire Lotharingien de Combinatoire</a>, </li> <li> <a href="http://epubs.siam.org/sam-bin/dbq/toclist/SIDMA">SIAM Journal on Discrete Math.</a> [unfortunately you or your library need a subscription for this journal] </li> </ul> etc. These and many other free electronic resources are listed in the <a href="http://www.doaj.org">Directory of Open Access Journals</a> and in the Electronic Library / Journals section of <a href="http://www.emis.de/">EMIS</a>. There are a large number of other journals available on the Web that often contain sequences, but for which you (or your institution) need a subscription. The <a href="http://www.elsevier.com/locate/issn/0195-6698">European Journal of Combinatorics</a>, the <a href="http://www.chemweb.com/journals/kluwer/?action=toc&jcode=KLUWJOMC">Journal of Mathematical Chemistry</a> are just two of dozens that could be listed here. If you have access to a good library, you should be able to search these journals for new sequences or new references for existing sequences. </li> <li> Look for sequences with keyword "uned" or "obsc" and edit them! </li> <li> Look out for broken links in the OEIS. (<a href="http://home.snafu.de/tilman/xenulink.html">Xenu</a> is the best tool for doing this systematically.) When you find a bad link, be a detective and track down the new URL. </li> <li> Extend some of the sequences that need more terms: set the <a href="WebCam.html">WebCam</a> to browse the sequences that need extending, or use the <a href="index.html">main look-up page</a> to search for keyword:more. </li> <li> See the list of <a href="future.html">future projects</a>. </li> </ul> <hr> <a NAME="Z44">Q:</a> You asked people to help edit sequences with keyword "uned". What exactly do you need done? A: It is not easy to give a precise answer. The best thing would be to look at some well-written entries in the OEIS (here are some picked at random off the WebCam: <a href="A001316">A001316</a>, <a href="A055545">A055545</a>, <a href="A052402">A052402</a>, <a href="A007308">A007308</a>). Then look at the two web pages that describe the <a href="eishelp1.html">internal format</a> and the <a href="eishelp2.html">standard or beautified format</a> used in the replies from the lookup service. This is how things should be! Now look at some entries with keyword "uned". (Search <a href="index.html?q=keyword:uned">here</a>.) Usually you will see that many things are wrong! The description is obscure, or the entries are obviously wrong, or the English is hopeless, etc. To help, make a copy of the sequence in the internal format, edit it (very carefully) and email it to me (njasloane@gmail.com) using subject line "EDITED A012345" (say). Sequences that need a lot of work have keyword "uned", but there many others that could be improved. If you don't see anything wrong, send me email saying sequence A012345 (say) looks fine and doesn't need further editing. <hr> <a NAME="Z45">Q:</a> I am emailing you a corrected version of a sequence. Should I say "Edited by ...", "Extended by ...", or not sign it at all? A: If you just added more terms, say something like: <pre> %E A060031 More terms from Larry Reeves (larryr(AT)acm.org), Jan 01 2003 %E A070171 Corrected and extended by Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 02 2002 </pre> If you made some nontrivial changes, say something like: <pre> %E A067581 Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 03 2002 %E A069841 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 04 2002 %F A083741 G.f.: 3*(x-2)*ln(1-x)-5*x+x^2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 06 2003 %F A006721 a(n) is asymptotic to C^n with C=1.226....... - Benoit Cloitre (abcloitre(AT)wanadoo.fr), Aug 07 2002 </pre> Reasons for doing this: <ul> <li>So you get credit for the changes.</li> <li>So you can be contacted in case there is an error!</li> <li>To indicate that someone else besides the author has looked at the sequence and approved it.</li> <li>To indicate that it has been changed on that date.</li> </ul> <hr> <a NAME="Z46">Q:</a> How can one obtain a file of all the sequences (stripped of formatting) for running tests? A: Go to the <a href="Seis.html">Welcome</a> page, and scroll down. After a while you will see a link to a stripped-down and gzipped version of the database. <hr> <a NAME="Z33">Q:</a> Why are there no mirror sites? A: This is essentially a one-man operation, and it is hard enough to maintain one site. <hr> <a NAME="Z28">Q:</a> Can one subscribe to the comment mail queue? A: Not at present. But unless I am traveling, comments usually get processed within a few days. <hr> Thanks to all the sequence fans who suggested questions and answers for this page. </div></div> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome">Welcome</a> <a href="/wiki/Main_Page">Wiki</a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified November 23 22:07 EST 2024. 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