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 A121270 #18 Feb 16 2025 08:33:02
%S A121270 2,5,257
%N A121270 Prime Sierpinski numbers of the first kind: primes of the form k^k+1.
%C A121270 Sierpinski proved that k>1 must be of the form 2^(2^j) for k^k+1 to be a prime. All a(n) > 2 must be the Fermat numbers F(m) with m = j+2^j = A006127(j). [Edited by _Jeppe Stig Nielsen_, Jul 09 2023]
%D A121270 See e.g. pp. 156-157 in M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001. - _Walter Nissen_, Mar 20 2010
%H A121270 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html">Sierpinski Number of the First Kind</a>
%t A121270 Do[f=n^n+1;If[PrimeQ[f],Print[{n,f}]],{n,1,1000}]
%o A121270 (PARI) for(n=1,9,if(ispseudoprime(t=n^n+1),print1(t", "))) \\ _Charles R Greathouse IV_, Feb 01 2013
%Y A121270 Primes of form b*k^k + 1: this sequence (b=1), A216148 (b=2), A301644 (b=3), A301641 (b=4), A301642 (b=16).
%Y A121270 Cf. A014566, A048861, A006127, A000215.
%K A121270 nonn,bref
%O A121270 1,1
%A A121270 _Alexander Adamchuk_, Aug 23 2006
%E A121270 Definition rewritten by _Walter Nissen_, Mar 20 2010