1,2

Or, numbers written in base 1.

If p is a prime >5 then d_{a(p)} == 1 mod (p) where d_{a(p)} is a divisor of a(p). This also gives an alternate elementary proof of the infinitude of prime numbers by the fact that for every prime p there exists at least one prime of the form kp+1. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 05 2002

11=1*9+2; 111=12*9+3; 1111=123*9+4; 11111=1234*9+5; 111111=12345*9+6; 1111111=123456*9+7; 11111111=1234567*9+8; 111111111=12345678*9+9. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 17 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

K. G. Kroeber, Mathematik der Palindrome; p. 348; 2003; ISBN 3 499 615762; Rowohlt Verlag; Germany

D. Olivastro, Ancient Puzzles. Bantam Books, NY, 1993, p. 276.

Amarnath Murthy, On the divisors of the unary sequence, Smarandache Notions Journal Vol. - 11, 2000.

Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 2.12.

David Wasserman, Table of n, a(n) for n=1..1000

Index entries for sequences related to linear recurrences with constant coefficients

a(n) = (10^n-1)/9.

G.f.: 1/((1-x)*(1-10*x)).

Binomial transform of A003952. - Paul Barry (pbarry(AT)wit.ie), Jan 29 2004

a(n)=10a(n-1)+1, n>1, a(1)=1. [Offset 1]. a(n)=sum{k=0..n, binomial(n+1, k+1)9^k}. [Offset 0]. - Paul Barry (pbarry(AT)wit.ie), Aug 24 2004

a(2n) -2*a(n) ={3*a(n)}^2. a(6)-2*a(3) = {3*a(3)}^2. 111111-222 = 110889 - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 21 2003

a(n) = binary representation of n-th Mersenne number (A000225). - Ross La Haye (rlahaye(AT)new.rr.com), Sep 13 2003

The Hankel transform of this sequence is [1,-10,0,0,0,0,0,0,0,0,...] - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007

Table[(10^n - 1)/9, {n, 1, 18}]

(PARI) a(n)=if(n<0, 0, (10^n-1)/9)

(Other) sage: [gaussian_binomial(n, 1, 10) for n in xrange(1, 19)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]

Cf. A002275, A007088, A007089, A007090, A007091, A007092, A007093, A007094 & A007095.

Sequence in context: A165370 A134962 A113589 this_sequence A135463 A002275 A078998

Adjacent sequences: A000039 A000040 A000041 this_sequence A000043 A000044 A000045

easy,nonn,nice

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

More terms from Paul Barry (pbarry(AT)wit.ie), Jan 29 2004