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A122000 a(n) = ((2^n - 1)^(2^n - 1) + 1) / 2^n. 3
1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, 3566766192921360077810945505268211287512797261288920841093043641769808083046939618603793791988232043305924036607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..6.

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

FORMULA

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

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

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

MATHEMATICA

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

CROSSREFS

Cf. A014566, A081216, A056009.

Sequence in context: A110719 A158816 A173839 * A291906 A090769 A013842

Adjacent sequences:  A121997 A121998 A121999 * A122001 A122002 A122003

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Sep 11 2006

STATUS

approved

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Last modified December 8 16:57 EST 2021. Contains 349596 sequences. (Running on oeis4.)