A180362 - OEIS

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A180362

Primes of the form k * n^n + 1 with k < n^n.

5, 13, 109, 163, 257, 271, 379, 433, 487, 541, 769, 3329, 7681, 7937, 9473, 10753, 11777, 12289, 13313, 14081, 14593, 15361, 17921, 18433, 19457, 22273, 23041, 23297, 25601, 26113, 26881, 30977, 31489, 32257, 36097, 36353, 37501, 37633, 37889, 39937, 40193

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OFFSET

1,1

COMMENTS

A result of Heath-Brown shows, on the GRH, that this sequence is infinite; can this be proved unconditionally? The averaged result of Bombieri-Friedlander-Iwaniec does not seem to be strong enough.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proceedings of the London Mathematical Society 64:3 (1992), pp. 265-338.

FORMULA

k * n^n + 1, where k < n^n.

EXAMPLE

a(4) = 109, because 4 * 3^3 + 1 = 109, which is prime, and 4 < 27.

PROG

(PARI) isA180362(n)=my(b=2); while(b^b<n, if(n%(b^b)==1 && n < b^(2*b), return(isprime(n))); b++); 0

CROSSREFS

Sequence in context: A117437 A179089 A106046 * A117527 A228280 A155175

Adjacent sequences: A180359 A180360 A180361 * A180363 A180364 A180365