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A125598 a(n) = ((n+1)^(n-1)-1)/n. 2
0, 1, 5, 31, 259, 2801, 37449, 597871, 11111111, 235794769, 5628851293, 149346699503, 4361070182715, 139013933454241, 4803839602528529, 178901440719363487, 7143501829211426575, 304465936543600121441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Odd prime p divides a(p-2).

a(n) is prime for n = {3,4,6,74,...}; prime terms are {5, 31, 2801, ...}.

a(n) is the (n-1)-th generalized repunit in base (n+1). For example, a(5) = 259 which is 1111 in base 6. - Mathew Englander, Oct 20 2020

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) = ((n+1)^(n-1)-1)/n.

a(n) = (A000272(n+1)-1)/n.

a(2k-1)/(2k+1) = A125599(k) for k>0.

From Mathew Englander, Dec 17 2020: (Start)

a(n) = (A060072(n+1) - A083069(n-1))/2.

For n > 1, a(n) = Sum_{k=0..n-2} (n+1)^k.

For n > 1, a(n) = Sum_{j=0..n-2} n^j*C(n-1,j+1).

(End)

MAPLE

a:=n->sum((n+3)^j, j=0..n): seq(a(n), n=-1..17); # Zerinvary Lajos, Dec 17 2008

MATHEMATICA

Table[((n+1)^(n-1)-1)/n, {n, 1, 25}]

PROG

(Sage) [gaussian_binomial(n, 1, n+2) for n in range(0, 18)] # Zerinvary Lajos, May 31 2009

CROSSREFS

Cf. A000272 (n^(n-2)), A125599.

Cf. other sequences of generalized repunits, such as A125118, A053696, A055129, A060072, A031973, A173468, A023037, A119598, A085104, and A162861.

Sequence in context: A279434 A000556 A320512 * A267436 A294215 A294216

Adjacent sequences:  A125595 A125596 A125597 * A125599 A125600 A125601

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Nov 26 2006

STATUS

approved

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Last modified January 23 05:47 EST 2021. Contains 340384 sequences. (Running on oeis4.)