A122000 a(n) = ((2^n - 1)^(2^n - 1) + 1) / 2^n.

1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, 3566766192921360077810945505268211287512797261288920841093043641769808083046939618603793791988232043305924036607

Offset: 1

Author

Alexander Adamchuk, Sep 11 2006

Keywords

• nonn

Comments

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, Jan 22 2007

Links

• Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind.

Crossrefs

Cf. A014566, A081216, A056009.

Programs

Mathematica

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

Formula

a(n) = A014566(2^n - 1) / 2^n.

a(n) = A081216(2^n - 1).

a(n) = A056009(2^n - 1).