A193813 Least k such that n^n + k + 1 is a prime.

0, 0, 1, 0, 11, 6, 3, 42, 9, 18, 61, 34, 15, 26, 27, 12, 73, 106, 17, 90, 31, 86, 13, 94, 95, 42, 67, 134, 119, 18, 57, 6, 57, 62, 53, 30, 41, 114, 9, 156, 109, 12, 3, 402, 121, 456, 533, 36, 17, 30, 225, 252, 19, 192, 101, 176, 391, 44, 193, 256, 101, 78, 453

Offset: 1

Author

Michel Lagneau, Aug 06 2011

Keywords

• nonn

Examples

			a(5) = 11 because 5^5 + 11 + 1 = 37 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000312, A098682.

Programs

Mathematica

a={};Do[k = 0; While[ !PrimeQ[n^n + k + 1], k++ ]; AppendTo[a, k], {n, 1, 100} ];a

PARI

a(n) = nextprime(n^n) - n^n - 1; \\ Michel Marcus, Aug 20 2019

Formula

a(n) = A098682(n) - n^n -1. - Michel Marcus, Aug 20 2019