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 A124899 #27 Feb 16 2025 08:33:03
%S A124899 1,7,521,102943,38742049,23775972551,21633936185161,27368368148803711,
%T A124899 45957792327018709121,98920982783015679456199,
%U A124899 265572137199362841880960201,870019499993663001431459704607,3416070845000481662841943594125601
%N A124899 Sierpinski quotient ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n).
%C A124899 2n divides Sierpinski number A014566(2n-1).
%C A124899 2^n divides A014566(2^n-1); A014566(2^n - 1) / 2^n = A081216(2^n - 1) = A122000(n) = {1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, ...}.
%C A124899 p+1 divides A014566(p) for prime p; A014566(p)/(p+1) = A056852(n) = {7, 521, 102943, 23775972551, 21633936185161, ...}.
%C A124899 Primes in this sequence are {7, 521, 45957792327018709121}.
%H A124899 Seiichi Manyama, <a href="/A124899/b124899.txt">Table of n, a(n) for n = 1..194</a>
%H A124899 Eric Weisstein, World of Mathematics. <a href="https://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html">Sierpinski Numbers of the First Kind</a>.
%F A124899 a(n) = ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n).
%F A124899 (2n-1)^(a(n)-1) == 1 (mod a(n)). - _Thomas Ordowski_, Mar 16 2021
%p A124899 seq(((2*n-1)^(2*n-1)+1)/(2*n),n=1..20); # _Muniru A Asiru_, Apr 08 2018
%t A124899 Table[((2n-1)^(2n-1)+1)/(2n),{n,1,20}]
%o A124899 (GAP) List([1..15],n->((2*n-1)^(2*n-1)+1)/(2*n)); # _Muniru A Asiru_, Apr 08 2018
%o A124899 (PARI) a(n) = ((2*n-1)^(2*n-1) + 1)/(2*n); \\ _Michel Marcus_, Apr 08 2018
%Y A124899 Cf. A014566 (Sierpinski numbers of the first kind: n^n + 1).
%Y A124899 Cf. A056826, A056852, A081216, A122000.
%K A124899 nonn
%O A124899 1,2
%A A124899 _Alexander Adamchuk_, Nov 12 2006