This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A122000 #10 Feb 16 2025 08:33:02
%S A122000 1,7,102943,27368368148803711,
%T A122000 533411691585101123706582594658103586126397951,
%U A122000 3566766192921360077810945505268211287512797261288920841093043641769808083046939618603793791988232043305924036607
%N A122000 a(n) = ((2^n - 1)^(2^n - 1) + 1) / 2^n.
%C A122000 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).
%C A122000 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
%H A122000 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html">Sierpinski Number of the First Kind</a>.
%F A122000 a(n) = A014566(2^n - 1) / 2^n.
%F A122000 a(n) = A081216(2^n - 1).
%F A122000 a(n) = A056009(2^n - 1).
%t A122000 Table[((2^n-1)^(2^n-1)+1)/2^n,{n,1,7}]
%Y A122000 Cf. A014566, A081216, A056009.
%K A122000 nonn
%O A122000 1,2
%A A122000 _Alexander Adamchuk_, Sep 11 2006