A121270 Prime Sierpinski numbers of the first kind: primes of the form k^k+1.

2, 5, 257

Offset: 1

Author

Alexander Adamchuk, Aug 23 2006

Keywords

• nonn
• bref

Comments

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]

References

• 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

Links

• Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind

Crossrefs

Primes of form b*k^k + 1: this sequence (b=1), A216148 (b=2), A301644 (b=3), A301641 (b=4), A301642 (b=16).

Cf. A014566, A048861, A006127, A000215.

Programs

Mathematica

Do[f=n^n+1;If[PrimeQ[f],Print[{n,f}]],{n,1,1000}]

PARI

for(n=1,9,if(ispseudoprime(t=n^n+1),print1(t", "))) \\ Charles R Greathouse IV, Feb 01 2013

Extensions

Definition rewritten by Walter Nissen, Mar 20 2010