A118925 a(n) is the least prime p such that n*((p#)^5)-1 is prime, or 0 if n > 1 is a 5th power so no prime possible.

2, 3, 3, 2, 347, 2, 2, 3, 389, 29, 13, 2, 7, 3, 2, 269, 1091, 3, 2, 5, 67, 337, 11, 5, 31, 5, 2, 3, 3, 3, 2, 0, 131, 2, 5, 2, 71, 389, 229, 2, 29, 109, 43, 3, 2, 2, 3, 137, 2, 5, 47, 2, 3, 7, 2, 163, 2, 397, 2767, 13, 2, 5, 3, 3, 73, 2, 2, 13, 2, 2, 23, 29, 733, 5, 2, 607, 5, 3, 7, 5, 2, 17

Offset

1,1

Links

Table of n, a(n) for n=1..82.

Example

1*(2^5)-1 = 31, 31 is prime, so a(1) = 2.
2*((2*3)^5)-1 = 15551, 15551 is prime, so a(2) = 3.
3*((2*3)^5)-1 = 23327, 23327 is prime, so a(3) = 3.

Mathematica

a[n_] := If[n > 1 && IntegerQ[Surd[n, 5]], 0, Module[{p = pr = 2}, While[! PrimeQ[n*pr^5 - 1], p = NextPrime[p]; pr *= p]; p]]; Array[a, 100] (* Amiram Eldar, Sep 11 2021 *)

Crossrefs

Cf. A118664 (with squares), A118665 (with cubes).

Sequence in context: A153592 A351188 A153878 * A308100 A351065 A171576

Adjacent sequences: A118922 A118923 A118924 * A118926 A118927 A118928

Keyword

nonn

Author

Pierre CAMI, May 25 2006

Extensions

Data corrected by Amiram Eldar, Sep 11 2021

Status

approved