

A122000


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


3



1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, 3566766192921360077810945505268211287512797261288920841093043641769808083046939618603793791988232043305924036607
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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(p1) for prime p>2. Corresponding quotients are a(p1) / (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^n1)^(2^n1)+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



