A118665 a(n) is the least prime p such that n*(p#^3)-1 is prime or 0 if n > 1 is a cube so no prime possible.

2, 3, 2, 2, 5, 2, 3, 0, 2, 2, 59, 3, 2, 3, 11, 2, 3, 19, 2, 401, 2, 3, 3, 2, 2, 7, 0, 2, 3, 2, 13, 3, 2, 2, 3, 7, 7, 11, 2, 5, 5, 17, 7, 5, 2, 2, 3, 2, 31, 3, 13, 257, 3, 2, 2, 5, 41, 2, 3, 2, 2, 31, 2, 0, 3359, 47, 19, 31, 17, 5, 13, 3, 3, 5, 2, 2, 3, 41, 2, 31

Offset

1,1

Links

Table of n, a(n) for n=1..80.

Example

1*(2^3)-1 = 7 is prime, so a(1) = 2.
2*(2^3)-1 = 15 is composite, 2*((2*3)^3)-1 = 431 is prime, so a(2) = 3.

Mathematica

a[n_] := If[n>1 && IntegerQ[Surd[n, 3]], 0, Module[{p = pr = 2}, While[!PrimeQ[n * pr^3 - 1], p = NextPrime[p]; pr *= p]; p]]; Array[a, 100] (* Amiram Eldar, Sep 11 2021 *)

Prog

(PARI) pr(p) = my(pr=1); forprime(q=2, p, pr *= q); pr;
a(n) = if (ispower(n, 3) && (n>1), return (0)); my(p=2); while (!ispseudoprime(n*pr(p)^3-1), p = nextprime(p+1)); p; \\ Michel Marcus, Sep 11 2021

Crossrefs

Cf. A118664 (with squares), A118925 (with 5th powers).

Sequence in context: A225176 A349271 A349387 * A333238 A336526 A225243

Adjacent sequences: A118662 A118663 A118664 * A118666 A118667 A118668

Keyword

nonn

Author

Pierre CAMI, May 19 2006

Extensions

Data corrected and more terms added by Amiram Eldar, Sep 11 2021

Status

approved