Search: id:A002275
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%I A002275
%S A002275 0,1,11,111,1111,11111,111111,1111111,11111111,111111111,1111111111,11111111111,
%T A002275 111111111111,1111111111111,11111111111111,111111111111111,1111111111111111,
%U A002275 11111111111111111,111111111111111111,1111111111111111111,11111111111111111111
%N A002275 Repunits: (10^n - 1)/9. Often denoted by R_n.
%C A002275 R_n is a string of n 1's.
%C A002275 Base 4 representation of Jacobsthal bisection sequence A002450. E.g. 
               a(4)= 1111 because A002450(4)= 85 (in base 10) = 64 + 16 + 4 + 1 
               = 1*(4^3)+1*(4^2)+1*(4^1)+1. - Paul Barry (pbarry(AT)wit.ie), Mar 
               12 2004
%C A002275 Except for the first two terms, these numbers cannot be perfect squares, 
               because x^2 =/= 11 (mod 100) - Zak Seidov (zakseidov(AT)yahoo.com), 
               Dec 05 2008.
%C A002275 For n >= 2: a(n) = Sequence A000225(n) written in base 2. [From Jaroslav 
               Krizek (jaroslav.krizek(AT)atlas.cz), Jul 27 2009]
%D A002275 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, 
               pp. 197-8 Penguin Books 1987.
%H A002275 David Wasserman, <a href="b002275.txt">Table of n, a(n) for n=0..1000</
               a>
%H A002275 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A002275 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Link to a section of The World of Mathematics.</a>
%H A002275 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DemloNumber.html">Demlo Number</a>
%F A002275 a(n)=10a(n-1)+1, a(0)=0.
%F A002275 Second binomial transform of Jacobsthal trisection A001045(3n)/3 (A015565). 
               - Paul Barry (pbarry(AT)wit.ie), Mar 24 2004
%F A002275 a(n)=11*a(n-1)-10*a(n-2);a(0)=0,a(1)=1. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jun 07 2006
%F A002275 G.f. x/((1-10x)(1-x)). Regarded as base b numbers, g.f. x/((1-bx)(1-x)). 
               - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 15 2006
%F A002275 a(n) = A125118(n,9) for n>8. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 21 2006
%p A002275 a:=n->sum(10^(n-j),j=1..n): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 04 2007
%t A002275 lst={};Do[p=(10^n-1)/9;AppendTo[lst, p], {n, 0, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Sep 28 2008]
%o A002275 (Other) sage: [lucas_number1(n,11,10) for n in xrange(0, 21)]# [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
%o A002275 (Other) sage: [gaussian_binomial(n,1,10) for n in xrange(0,20)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%o A002275 (PARI) A002275(n) = (10^n-1)/9 [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Oct 26 2009]
%Y A002275 Cf. A000042. Partial sums of 10^n (A011557). Factors: A003020, A067063.
%Y A002275 Bisections give A099814, A100706.
%Y A002275 Cf. A046053; A095370.
%Y A002275 Sequence in context: A113589 A000042 A135463 this_sequence A078998 A078191 
               A097115
%Y A002275 Adjacent sequences: A002272 A002273 A002274 this_sequence A002276 A002277 
               A002278
%K A002275 easy,nonn,nice,core
%O A002275 0,3
%A A002275 N. J. A. Sloane (njas(AT)research.att.com).

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