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A060072 a(n) = (n^(n-1) - 1)/(n-1) for n>1, a(1) = 0. 16
0, 1, 4, 21, 156, 1555, 19608, 299593, 5380840, 111111111, 2593742460, 67546215517, 1941507093540, 61054982558011, 2085209001813616, 76861433640456465, 3041324492229179280, 128583032925805678351, 5784852794328402307380, 275941052631578947368421 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
(n-1)-digit repunits in base n written in decimal.
LINKS
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. 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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Feb 21 2001
EXTENSIONS
Name edited by Michel Marcus, Dec 14 2020
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)