%I #17 Jul 09 2023 09:57:10
%S 2,5,257
%N Prime Sierpinski numbers of the first kind: primes of the form k^k+1.
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html">Sierpinski Number of the First Kind</a>
%t Do[f=n^n+1;If[PrimeQ[f],Print[{n,f}]],{n,1,1000}]
%o (PARI) for(n=1,9,if(ispseudoprime(t=n^n+1),print1(t", "))) \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Primes of form b*k^k + 1: this sequence (b=1), A216148 (b=2), A301644 (b=3), A301641 (b=4), A301642 (b=16).
%Y Cf. A014566, A048861, A006127, A000215.
%K nonn,bref
%O 1,1
%A _Alexander Adamchuk_, Aug 23 2006
%E Definition rewritten by _Walter Nissen_, Mar 20 2010