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A121270 Prime Sierpinski numbers of the first kind: primes of the form k^k+1. 10
2, 5, 257 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sierpinski proved that n must be of the form 2^2^k for n^n+1 to be a prime. All a(n) must be the Fermat numbers F(m) with m = k+2^k = A006127(k).

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

Table of n, a(n) for n=1..3.

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

MATHEMATICA

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

PROG

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

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.

Sequence in context: A137068 A137066 A175977 * A085603 A309675 A042341

Adjacent sequences:  A121267 A121268 A121269 * A121271 A121272 A121273

KEYWORD

nonn,bref

AUTHOR

Alexander Adamchuk, Aug 23 2006

EXTENSIONS

Definition rewritten by Walter Nissen, Mar 20 2010

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)