A056009 -id:A056009 - cp's OEIS frontend

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

1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, 3566766192921360077810945505268211287512797261288920841093043641769808083046939618603793791988232043305924036607

Offset: 1

Alexander Adamchuk, Sep 11 2006

nonn

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

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

Cf. A014566, A081216, A056009.

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

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

A128446 Quotients A122000(p-1) / (2^p - 1), where p = prime(n) for n > 1.

Original entry on oeis.org

1, 882850585445281, 28084773172609134470952326813135521948919663474715912134590894817085103016117634792155856629828598766188378241

Offset: 2

Alexander Adamchuk, Mar 03 2007

A014566(n) = n^n + 1 is a Sierpinski Number of the First Kind.
A014566(2^n - 1) is divisible by 2^n.
A122000(n) = ((2^n - 1)^(2^n - 1) + 1) / 2^n = A014566(2^n - 1) / 2^n = A081216(2^n - 1).
a(5) = 6.044...*10^3072, and is too large to include. - Amiram Eldar, Jul 17 2025

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

Cf. A122000, A014566, A081216, A056009.

a[n_] := Module[{p = Prime[n]}, ((2^(p-1) - 1)^(2^(p-1) - 1) + 1)/(2^(p-1)*(2^p-1))]; Array[a, 3, 2] (* Amiram Eldar, Jul 17 2025 *)

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

cp's OEIS Frontend

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

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