0,3

R_n is a string of n 1's.

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

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.

For n >= 2: a(n) = Sequence A000225(n) written in base 2. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jul 27 2009]

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 197-8 Penguin Books 1987.

David Wasserman, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Demlo Number

a(n)=10a(n-1)+1, a(0)=0.

Second binomial transform of Jacobsthal trisection A001045(3n)/3 (A015565). - Paul Barry (pbarry(AT)wit.ie), Mar 24 2004

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

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

a(n) = A125118(n,9) for n>8. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 21 2006

a:=n->sum(10^(n-j), j=1..n): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007

lst={}; Do[p=(10^n-1)/9; AppendTo[lst, p], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 28 2008]

(Other) sage: [lucas_number1(n, 11, 10) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]

(Other) sage: [gaussian_binomial(n, 1, 10) for n in xrange(0, 20)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]

(PARI) A002275(n) = (10^n-1)/9 [From Michael Porter (michael_b_porter(AT)yahoo.com), Oct 26 2009]

Cf. A000042. Partial sums of 10^n (A011557). Factors: A003020, A067063.

Bisections give A099814, A100706.

Cf. A046053; A095370.

Sequence in context: A113589 A000042 A135463 this_sequence A078998 A078191 A097115

Adjacent sequences: A002272 A002273 A002274 this_sequence A002276 A002277 A002278

easy,nonn,nice,core

N. J. A. Sloane (njas(AT)research.att.com).