A060072 a(n) = (n^(n-1) - 1)/(n-1) for n>1, a(1) = 0.

0, 1, 4, 21, 156, 1555, 19608, 299593, 5380840, 111111111, 2593742460, 67546215517, 1941507093540, 61054982558011, 2085209001813616, 76861433640456465, 3041324492229179280, 128583032925805678351, 5784852794328402307380, 275941052631578947368421

Offset

1,3

Comments

(n-1)-digit repunits in base n written in decimal.

Links

Harry J. Smith, Table of n, a(n) for n=1..200

Formula

a(n+1) = Sum_{k=1..n} n^(k-1)*C(n, k). - Olivier Gérard, Jun 26 2001 [Corrected by Mathew Englander, Dec 15 2020]

a(n) = Sum_{j=2..n} n^(n-j). - Zerinvary Lajos, Sep 11 2006

a(n+1) = A125118(n,n). - Reinhard Zumkeller, Nov 21 2006

a(n) = Integral_{x=1/n..1} 1/x^n dx. - Francesco Daddi, Aug 01 2011

a(n) = A037205(n-1)/(n-1) = A060073(n)*(n-1) = A023037(n) - A000169(n).

a(n) = [x^n] x^2/((1 - x)*(1 - n*x)). - Ilya Gutkovskiy, Oct 04 2017

a(n) = 1 + A228275(n, n-2) for n >= 2. - Mathew Englander, Dec 14 2020

Example

a(10)=111111111; i.e., just nine 1's (converted from base 10 to decimal).

Mathematica

Join[{0}, Array[(#^(#-1)-1)/(#-1)&, 20, 2]] (* Harvey P. Dale, Jun 04 2013 *)

Prog

(PARI) a(n) = if (n==1, 0, (n^(n - 1) - 1)/(n - 1)); \\ Harry J. Smith, Jul 01 2009
(Magma) [0] cat [ (n^(n-1) -1)/(n-1) : n in [2..25]]; // G. C. Greubel, Aug 15 2022
(SageMath) [0]+[(n^(n-1) -1)/(n-1) for n in (2..25)] # G. C. Greubel, Aug 15 2022

Crossrefs

Cf. A000169, A037205, A055869, A060073, A125118, A228275.

Cf. other sequences of generalized repunits, such as A053696, A055129, A031973, A125598, A173468, A023037, A119598, A085104, and A162861.

Sequence in context: A316370 A357424 A166901 * A157503 A144010 A366184

Adjacent sequences: A060069 A060070 A060071 * A060073 A060074 A060075

Keyword

nonn

Author

Henry Bottomley, Feb 21 2001

Extensions

Name edited by Michel Marcus, Dec 14 2020

Status

approved