A074966 a(n) = least k such that n^n + k is prime.

1, 1, 2, 1, 12, 7, 4, 43, 10, 19, 62, 35, 16, 27, 28, 13, 74, 107, 18, 91, 32, 87, 14, 95, 96, 43, 68, 135, 120, 19, 58, 7, 58, 63, 54, 31, 42, 115, 10, 157, 110, 13, 4, 403, 122, 457, 534, 37, 18, 31, 226, 253, 20, 193, 102, 177, 392, 45, 194, 257, 102, 79, 454, 231, 306

Offset: 1

Author

Zak Seidov, Oct 03 2002

Keywords

• nonn

Comments

"Are there any n except 1, 2 and 4 that make n^n + 1 a prime? He [Sierpiński] has shown that if such a prime exists it is greater than 10^30000." - Ogilvy and Anderson

References

• C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988. Page 82.

Links

• Hans Havermann and Seiichi Manyama, Table of n, a(n) for n = 1..2500 (Seiichi Manyama to 500)

Crossrefs

Cf. A055385, A074967.

Programs

Mathematica

Array[Block[{k = 1}, While[! PrimeQ[k + #], k++]; k] &[#^#] &, 65] (* Michael De Vlieger, Jul 06 2018 *)

PARI

a(n)=(x->nextprime(x)-x)(n^n) \\ Charles R Greathouse IV, Nov 25 2014

Extensions

More terms from Robert G. Wilson v, Oct 04 2002

Name taken from Comments section by Jon E. Schoenfield, Jan 14 2015