1,2

A014566[n] = n^n + 1 is Sierpinski Number of the First Kind. A014566[2^n - 1] is divisible by 2^n. a(n) is a subset of A081216[n] = (n^n-(-1)^n)/(n+1).

2^p - 1 divides a(p-1) for prime p>2. Corresponding quotients are a(p-1) / (2^p - 1) = {1, 882850585445281, 28084773172609134470952326813135521948919663474715912134590894817085103016117634792155856629828598766188378241, ...}, where p = Prime[n] for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 22 2007

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Sierpinski Number of the First Kind.

a(n) = ((2^n - 1)^(2^n - 1) + 1) / 2^n. a(n) = A014566[2^n - 1] / 2^n. a(n) = A081216[2^n - 1]. a(n) = A056009[2^n - 1].

Table[((2^n-1)^(2^n-1)+1)/2^n, {n, 1, 7}]

Cf. A014566, A081216, A056009.

Sequence in context: A123062 A110719 A158816 this_sequence A090769 A013842 A145322

Adjacent sequences: A121997 A121998 A121999 this_sequence A122001 A122002 A122003

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 11 2006