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A002275 - OEIS
<!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>A002275 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A002275" 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=%2fA002275">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="A002275 - 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> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A002275 </div> <div class=seqname> Repunits: (10^n - 1)/9. Often denoted by R_n. </div> </div> <div class=scorerefs> 1181 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111, 1111111111111111111, 11111111111111111111</div> <div class=seqdatalinks> (<a href="/A002275/list">list</a>; <a href="/A002275/graph">graph</a>; <a href="/search?q=A002275+-id:A002275">refs</a>; <a href="/A002275/listen">listen</a>; <a href="/history?seq=A002275">history</a>; <a href="/search?q=id:A002275&fmt=text">text</a>; <a href="/A002275/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,3</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>R_n is a string of n 1's.</div> <div class=sectline>Base-4 representation of Jacobsthal bisection sequence <a href="/A002450" title="a(n) = (4^n - 1)/3.">A002450</a>. E.g., a(4)= 1111 because <a href="/A002450" title="a(n) = (4^n - 1)/3.">A002450</a>(4)= 85 (in base 10) = 64 + 16 + 4 + 1 = 1*(4^3) + 1*(4^2) + 1*(4^1) + 1. - <a href="/wiki/User:Paul_Barry">Paul Barry</a>, Mar 12 2004</div> <div class=sectline>Except for the first two terms, these numbers cannot be perfect squares, because x^2 != 11 (mod 100). - <a href="/wiki/User:Zak_Seidov">Zak Seidov</a>, Dec 05 2008</div> <div class=sectline>For n >= 0: a(n) = (<a href="/A000225" title="a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)">A000225</a>(n) written in base 2). - <a href="/wiki/User:Jaroslav_Krizek">Jaroslav Krizek</a>, Jul 27 2009, edited by <a href="/wiki/User:M._F._Hasler">M. F. Hasler</a>, Jul 03 2020</div> <div class=sectline>Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=10, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - <a href="/wiki/User:Milan_Janjic">Milan Janjic</a>, Feb 21 2010</div> <div class=sectline>Except 0, 1 and 11, all these integers are Brazilian numbers, <a href="/A125134" title=""Brazilian" numbers ("les nombres br茅siliens" in French): numbers n such that there is a natural number b with 1 < b < n-1 ...">A125134</a>. - <a href="/wiki/User:Bernard_Schott">Bernard Schott</a>, Dec 24 2012</div> <div class=sectline>Numbers n such that 11...111 = R_n = (10^n - 1)/9 is prime are in <a href="/A004023" title="Indices of prime repunits: numbers k such that 11...111 (with k 1's) = (10^k - 1)/9 is prime.">A004023</a>. - <a href="/wiki/User:Bernard_Schott">Bernard Schott</a>, Dec 24 2012</div> <div class=sectline>The terms 0 and 1 are the only squares in this sequence, as a(n) == 3 (mod 4) for n>=2. - <a href="/wiki/User:Nehul_Yadav">Nehul Yadav</a>, Sep 26 2013</div> <div class=sectline>For n>=2 the multiplicative order of 10 modulo the a(n) is n. - <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Aug 20 2014</div> <div class=sectline>The above is a special case of the statement that the order of z modulo (z^n-1)/(z-1) is n, here for z=10. - <a href="/wiki/User:Joerg_Arndt">Joerg Arndt</a>, Aug 21 2014</div> <div class=sectline>From <a href="/wiki/User:Peter_Bala">Peter Bala</a>, Sep 20 2015: (Start)</div> <div class=sectline>Let d be a divisor of a(n). Let m*d be any multiple of d. Split the decimal expansion of m*d into 2 blocks of contiguous digits a and b, so we have m*d = 10^k*a + b for some k, where 0 <= k < number of decimal digits of m*d. Then d divides a^n - (-b)^n (see McGough). For example, 271 divides a(5) and we find 2^5 + 71^5 = 11*73*271*8291 and 27^5 + 1^5 = 2^2*7*31*61*271 are both divisible by 271. Similarly, 4*271 = 1084 and 10^5 + 84^5 = 2^5*31*47*271*331 while 108^5 + 4^5 = 2^12*7*31*61*271 are again both divisible by 271. (End)</div> <div class=sectline>Starting with the second term this sequence is the binary representation of the n-th iteration of the Rule 220 and 252 elementary cellular automaton starting with a single ON (black) cell. - <a href="/wiki/User:Robert_Price">Robert Price</a>, Feb 21 2016</div> <div class=sectline>If p > 5 is a prime, then p divides a(p-1). - <a href="/wiki/User:Thomas_Ordowski">Thomas Ordowski</a>, Apr 10 2016</div> <div class=sectline>0, 1 and 11 are only terms that are of the form x^2 + y^2 + z^2 where x, y, z are integers. In other words, a(n) is a member of <a href="/A004215" title="Numbers that are the sum of 4 but no fewer nonzero squares.">A004215</a> for all n > 2. - <a href="/wiki/User:Altug_Alkan">Altug Alkan</a>, May 08 2016</div> <div class=sectline>Except for the initial terms, the binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 737", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - <a href="/wiki/User:Robert_Price">Robert Price</a>, Mar 17 2017</div> <div class=sectline>The term "repunit" was coined by Albert H. Beiler in 1964. - <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Nov 13 2020</div> <div class=sectline>q-integers for q = 10. - <a href="/wiki/User:John_Keith">John Keith</a>, Apr 12 2021</div> <div class=sectline>Binomial transform of <a href="/A001019" title="Powers of 9: a(n) = 9^n.">A001019</a> with leading zero. - <a href="/wiki/User:Jules_Beauchamp">Jules Beauchamp</a>, Jan 04 2022</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964, chapter XI, p. 83.</div> <div class=sectline>David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1987, pp. 197-198.</div> <div class=sectline>Samuel Yates, Peculiar Properties of Repunits, J. Recr. Math. 2, 139-146, 1969.</div> <div class=sectline>Samuel Yates, Prime Divisors of Repunits, J. Recr. Math. 8, 33-38, 1975.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>David Wasserman, <a href="/A002275/b002275.txt">Table of n, a(n) for n = 0..1000</a></div> <div class=sectline>Eudes Antonio Costa and Fernando Soares Carvalho, <a href="https://doi.org/10.14393/BEJOM-v5-2024-72280">On repunit polynomials sequence</a>, Braz. Elec. J. Math. (2024). See pp. 2, 15.</div> <div class=sectline>Dmytro S. Inosov and Emil Vlas谩k, <a href="https://arxiv.org/abs/2410.21427">Cryptarithmically unique terms in integer sequences</a>, arXiv:2410.21427 [math.NT], 2024. See pp. 3, 18.</div> <div class=sectline>Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit">Factorizations of 11...11 (Repunit)</a>.</div> <div class=sectline>W. M. Snyder, <a href="http://www.jstor.org/stable/2321382">Factoring Repunits</a>, Am. Math. Monthly, Vol. 89, No. 7 (1982), pp. 462-466.</div> <div class=sectline>Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.2639620">On Repunits</a>, Politecnico di Torino (Italy, 2019).</div> <div class=sectline>Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2044">Composition Operations of Generalized Entropies Applied to the Study of Numbers</a>, International Journal of Sciences (2019) Vol. 8, No. 4, 87-92.</div> <div class=sectline>Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].</div> <div class=sectline>Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.</div> <div class=sectline>Eudes Antonio Costa, Douglas Catulio Santos, Paula Maria Machado Cruz Catarino, and Elen Viviani Pereira Spreafico, <a href="https://doi.org/10.5281/zenodo.14563273">On Gaussian and Quaternion Repunit Numbers</a>, Rev. Mat. UFOP (Brazil, 2024) Vol. 2. See p. 2.</div> <div class=sectline>Eudes Antonio Costa, Paula Maria Machado Cruz Catarino, and Douglas Catulio Santos, <a href="https://doi.org/10.3390/sym17010028">A Study of the Symmetry of the Tricomplex Repunit Sequence with Repunit Sequence</a>, Symmetry (2024) Vol. 17, No. 1, 28.</div> <div class=sectline>Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>.</div> <div class=sectline>Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DemloNumber.html">Demlo Number</a>.</div> <div class=sectline>Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>.</div> <div class=sectline>Wikipedia, <a href="http://en.wikipedia.org/wiki/Repunit">Repunit</a>.</div> <div class=sectline>Amin Witno, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Witno/witno6.html">A Family of Sequences Generating Smith Numbers</a>, J. Int. Seq. 16 (2013) #13.4.6.</div> <div class=sectline>Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>.</div> <div class=sectline>Samuel Yates, <a href="http://www.jstor.org/stable/2689643">The Mystique of Repunits</a>, Math. Mag., Vol. 51, No. 1 (1978), pp. 22-28.</div> <div class=sectline><a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a></div> <div class=sectline><a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.</div> <div class=sectline><a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a></div> <div class=sectline><a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).</div> <div class=sectline><a href="/index/Cor#core">Index entries for "core" sequences</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>a(n) = 10*a(n-1) + 1, a(0)=0.</div> <div class=sectline>a(n) = <a href="/A000042" title="Unary representation of natural numbers.">A000042</a>(n) for n >= 1.</div> <div class=sectline>Second binomial transform of Jacobsthal trisection <a href="/A001045" title="Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer ...">A001045</a>(3n)/3 (<a href="/A015565" title="a(n) = 7*a(n-1) + 8*a(n-2), a(0) = 0, a(1) = 1.">A015565</a>). - <a href="/wiki/User:Paul_Barry">Paul Barry</a>, Mar 24 2004</div> <div class=sectline>G.f.: x/((1-10*x)*(1-x)). Regarded as base b numbers, g.f. x/((1-b*x)*(1-x)). - <a href="/wiki/User:Franklin_T._Adams-Watters">Franklin T. Adams-Watters</a>, Jun 15 2006</div> <div class=sectline>a(n) = 11*a(n-1) - 10*a(n-2), a(0)=0, a(1)=1. - <a href="/wiki/User:Lekraj_Beedassy">Lekraj Beedassy</a>, Jun 07 2006</div> <div class=sectline>a(n) = <a href="/A125118" title="Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n.">A125118</a>(n,9) for n>8. - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Nov 21 2006</div> <div class=sectline>a(n) = <a href="/A075412" title="Squares of A002277.">A075412</a>(n)/<a href="/A002283" title="a(n) = 10^n - 1.">A002283</a>(n). - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, May 31 2010</div> <div class=sectline>a(n) = a(n-1) + 10^(n-1) with a(0)=0. - <a href="/wiki/User:Vincenzo_Librandi">Vincenzo Librandi</a>, Jul 22 2010</div> <div class=sectline>a(n) = <a href="/A242614" title="Triangle read by rows: row n contains numbers with sum of digits = n, and not greater than the n-th repunit (cf. A007953 and...">A242614</a>(n,<a href="/A242622" title="a(n) = number of numbers with digit sum n, not greater than the n-th repunit (cf. A052222).">A242622</a>(n)). - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Jul 17 2014</div> <div class=sectline>E.g.f.: (exp(9*x) - 1)*exp(x)/9. - <a href="/wiki/User:Ilya_Gutkovskiy">Ilya Gutkovskiy</a>, May 11 2016</div> <div class=sectline>a(n) = Sum_{k=0..n-1} 10^k. - <a href="/wiki/User:Torlach_Rush">Torlach Rush</a>, Nov 03 2020</div> <div class=sectline>Sum_{n>=1} 1/a(n) = <a href="/A065444" title="Decimal expansion of 9*Sum_{k>=1} 1/(10^k-1).">A065444</a>. - <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Nov 13 2020</div> </div> </div> <div class=section> <div class=sectname>MAPLE</div> <div class=sectbody> <div class=sectline>seq((10^k - 1)/9, k=0..30); # <a href="/wiki/User:Wesley_Ivan_Hurt">Wesley Ivan Hurt</a>, Sep 28 2013</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Table[(10^n - 1)/9, {n, 0, 19}] (* <a href="/wiki/User:Alonso_del_Arte">Alonso del Arte</a>, Nov 15 2011 *)</div> <div class=sectline>Join[{0}, Table[FromDigits[PadRight[{}, n, 1]], {n, 20}]] (* <a href="/wiki/User:Harvey_P._Dale">Harvey P. Dale</a>, Mar 04 2012 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) a(n)=(10^n-1)/9; \\ <a href="/wiki/User:Michael_B._Porter">Michael B. Porter</a>, Oct 26 2009</div> <div class=sectline>(PARI) x='x+O('x^99); concat(0, Vec(x/((1-10*x)*(1-x)))) \\ <a href="/wiki/User:Altug_Alkan">Altug Alkan</a>, Apr 10 2016</div> <div class=sectline>(Sage) [lucas_number1(n, 11, 10) for n in range(21)] # <a href="/wiki/User:Zerinvary_Lajos">Zerinvary Lajos</a>, Apr 27 2009</div> <div class=sectline>(Haskell)</div> <div class=sectline>a002275 = (`div` 9) . subtract 1 . (10 ^)</div> <div class=sectline>a002275_list = iterate ((+ 1) . (* 10)) 0</div> <div class=sectline>-- <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Jul 05 2013, Feb 05 2012</div> <div class=sectline>(Maxima)</div> <div class=sectline>a[0]:0$</div> <div class=sectline>a[1]:1$</div> <div class=sectline>a[n]:=11*a[n-1]-10*a[n-2]$</div> <div class=sectline><a href="/A002275" title="Repunits: (10^n - 1)/9. Often denoted by R_n.">A002275</a>(n):=a[n]$</div> <div class=sectline>makelist(<a href="/A002275" title="Repunits: (10^n - 1)/9. Often denoted by R_n.">A002275</a>(n), n, 0, 30); /* <a href="/wiki/User:Martin_Ettl">Martin Ettl</a>, Nov 05 2012 */</div> <div class=sectline>(Magma) [(10^n-1)/9: n in [0..25]]; // <a href="/wiki/User:Vincenzo_Librandi">Vincenzo Librandi</a>, Nov 06 2014</div> <div class=sectline>(Python)</div> <div class=sectline>print([(10**n-1)//9 for n in range(100)]) # <a href="/wiki/User:Michael_S._Branicky">Michael S. Branicky</a>, Apr 30 2022</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Partial sums of 10^n (<a href="/A011557" title="Powers of 10: a(n) = 10^n.">A011557</a>). Factors: <a href="/A003020" title="Largest prime factor of the "repunit" number 11...1 (cf. A002275).">A003020</a>, <a href="/A067063" title="Smallest prime factor of repunit(n) = (10^n-1)/9 (A002275).">A067063</a>.</div> <div class=sectline>Bisections give <a href="/A099814" title="Bisection of A002275.">A099814</a>, <a href="/A100706" title="Bisection of A002275.">A100706</a>.</div> <div class=sectline>Cf. <a href="/A000042" title="Unary representation of natural numbers.">A000042</a>, <a href="/A046053" title="Total number of prime factors of the repunit R(n) = (10^n-1)/9.">A046053</a>, <a href="/A095370" title="Number of distinct prime factors of the repunit (-1 + 10^n)/9.">A095370</a>, <a href="/A002276" title="a(n) = 2*(10^n - 1)/9.">A002276</a>, <a href="/A002277" title="a(n) = 3*(10^n - 1)/9.">A002277</a>, <a href="/A002278" title="a(n) = 4*(10^n - 1)/9.">A002278</a>, <a href="/A002279" title="a(n) = 5*(10^n - 1)/9.">A002279</a>, <a href="/A002280" title="a(n) = 6*(10^n - 1)/9.">A002280</a>, <a href="/A002281" title="a(n) = 7*(10^n - 1)/9.">A002281</a>, <a href="/A002282" title="a(n) = 8*(10^n - 1)/9.">A002282</a>, <a href="/A059988" title="a(n) = (10^n - 1)^2.">A059988</a>, <a href="/A065444" title="Decimal expansion of 9*Sum_{k>=1} 1/(10^k-1).">A065444</a>, <a href="/A075415" title="Squares of A002280 or numbers (666...6)^2.">A075415</a>, <a href="/A178635" title="a(n) = 72 * ((10^n - 1)/9)^2.">A178635</a>, <a href="/A102380" title="Irregular triangle read by rows in which row n lists prime factors (with multiplicity) of the repunit (10^n - 1)/9 (A002275(n)).">A102380</a>, <a href="/A204845" title="Irregular triangle read by rows in which row n lists primitive prime factors of the repunit (10^n - 1)/9 (A002275(n)).">A204845</a>, <a href="/A204846" title="Irregular triangle read by rows in which row n lists algebraic prime factors of the repunit (10^n - 1)/9 (A002275(n)).">A204846</a>, <a href="/A204847" title="Primitive cofactor of n-th repunit A002275(n).">A204847</a>, <a href="/A204848" title="Algebraic cofactor of n-th repunit A002275(n).">A204848</a>, <a href="/A083278" title="Repunit powers.">A083278</a>, <a href="/A206244" title="Number of partitions of n into repunits (A002275).">A206244</a>, <a href="/A125134" title=""Brazilian" numbers ("les nombres br茅siliens" in French): numbers n such that there is a natural number b with 1 < b < n-1 ...">A125134</a>, <a href="/A004023" title="Indices of prime repunits: numbers k such that 11...111 (with k 1's) = (10^k - 1)/9 is prime.">A004023</a>.</div> <div class=sectline>Numbers having multiplicative digital roots 0-9: <a href="/A034048" title="Numbers with multiplicative digital root value 0.">A034048</a>, <a href="/A002275" title="Repunits: (10^n - 1)/9. Often denoted by R_n.">A002275</a>, <a href="/A034049" title="Numbers with multiplicative digital root value 2.">A034049</a>, <a href="/A034050" title="Numbers with multiplicative digital root value 3.">A034050</a>, <a href="/A034051" title="Numbers with multiplicative digital root value 4.">A034051</a>, <a href="/A034052" title="Numbers with multiplicative digital root value 5.">A034052</a>, <a href="/A034053" title="Numbers with multiplicative digital root value 6.">A034053</a>, <a href="/A034054" title="Numbers with multiplicative digital root value 7.">A034054</a>, <a href="/A034055" title="Numbers with multiplicative digital root value 8.">A034055</a>, <a href="/A034056" title="Numbers with multiplicative digital root value 9.">A034056</a>.</div> <div class=sectline>Sequence in context: <a href="/A366394" title="a(n) is the smallest number that can be obtained by deleting n digits from A007908(n).">A366394</a> <a href="/A135463" title="Numbers n with property that for each single digit d of n, we can also see the decimal expansions of d^2 and d^3 as substrin...">A135463</a> <a href="/A000042" title="Unary representation of natural numbers.">A000042</a> * <a href="/A294348" title="Sum of products of terms in all partitions of 10*n into powers of 10.">A294348</a> <a href="/A078998" title="Choose a(n) so that a(1)+a(2)+...+a(n) = concatenation of n first natural numbers.">A078998</a> <a href="/A078191" title="a(n) = concatenation of n n times divided by n.">A078191</a></div> <div class=sectline>Adjacent sequences: <a href="/A002272" title="Theta series of 32-dimensional Quebbemann lattice Q_32.">A002272</a> <a href="/A002273" title="Theta series of 28-dimensional Quebbemann lattice.">A002273</a> <a href="/A002274" title="Numbers k such that 57*2^k + 1 is prime.">A002274</a> * <a href="/A002276" title="a(n) = 2*(10^n - 1)/9.">A002276</a> <a href="/A002277" title="a(n) = 3*(10^n - 1)/9.">A002277</a> <a href="/A002278" title="a(n) = 4*(10^n - 1)/9.">A002278</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="it is very easy to produce terms of sequence">easy</span>,<span title="a sequence of nonnegative numbers">nonn</span>,<span title="an exceptionally nice sequence">nice</span>,<span title="an important sequence">core</span>,<span title="edited within the last two weeks">changed</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:N._J._A._Sloane">N. J. A. Sloane</a></div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></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 March 1 17:50 EST 2025. Contains 381311 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>