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 A014566 #41 Feb 16 2025 08:32:33
%S A014566 2,2,5,28,257,3126,46657,823544,16777217,387420490,10000000001,
%T A014566 285311670612,8916100448257,302875106592254,11112006825558017,
%U A014566 437893890380859376,18446744073709551617,827240261886336764178,39346408075296537575425,1978419655660313589123980
%N A014566 Sierpiński numbers of the first kind: n^n + 1.
%C A014566 Sierpiński primes of the form n^n + 1 are {2,5,257,...} = A121270. The prime p divides a((p-1)/2) for p = {5,7,13,23,29,31,37,47,53,61,71,...} = A003628 Primes congruent to {5, 7} mod 8. p^2 divides a((p-1)/2) for prime p = {29,37,3373,...}. - _Alexander Adamchuk_, Sep 11 2006
%C A014566 n divides a(n-1) for even n, or 2n divides a(2n-1). a(2n-1)/(2n) = A124899(n) = {1, 7, 521, 102943, 38742049, 23775972551, 21633936185161, 27368368148803711, 45957792327018709121, ...}. 2^n divides a(2^n-1). A014566[2^n - 1] / 2^n = A081216[2^n - 1] = A122000[n] = {1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, ...}. p+1 divides a(p) for prime p. a(p)/(p+1) = A056852[n] = {7, 521, 102943, 23775972551, 21633936185161, ...}. p^2 divides a((p-1)/2) for prime p = {29, 37, 3373} = A121999(n). - _Alexander Adamchuk_, Nov 12 2006
%D A014566 Graham Everest, Alf van der Poorten, Igor Shparlinski and Thomas Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%D A014566 Maohua Le, Primes in the sequences n^n+1 and n^n-1, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, pp. 156-157.
%D A014566 Paulo Ribenboim, The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 74, 1989.
%H A014566 M. F. Hasler, <a href="/A014566/b014566.txt">Table of n, a(n) for n = 0..100</a>
%H A014566 Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, Xiquan Publ. Hse., 1990, Problem 17.
%H A014566 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html">Sierpiński Number of the First Kind</a>.
%F A014566 For n>0, resultant of x^n+1 and nx-1. - _Ralf Stephan_, Nov 20 2004
%F A014566 E.g.f.: exp(x) + 1/(1+LambertW(-x)). - _Vaclav Kotesovec_, Dec 20 2014
%F A014566 Sum_{n>=1} 1/a(n) = A134883. - _Amiram Eldar_, Nov 15 2020
%t A014566 a(0) = 2; for n>0 Table[n^n+1,{n,1,20}] (* _Alexander Adamchuk_, Sep 11 2006 *)
%o A014566 (PARI) A014566(n)=n^n+1 /* _M. F. Hasler_, Jan 21 2009 */
%o A014566 (Maxima) A014566[n]:=if n=0 then 2 else n^n+1$
%o A014566 makelist(A014566[n],n,0,30); /* _Martin Ettl_, Oct 29 2012 */
%Y A014566 Cf. A000312, A048861, A121270, A003628, A122000, A081216, A056852, A121999, A124899, A134883.
%K A014566 nonn,easy
%O A014566 0,1
%A A014566 _Eric W. Weisstein_
%E A014566 More terms from _Erich Friedman_