A238848 Smallest k such that k*n^3 - 1 is prime.

3, 1, 2, 2, 4, 2, 14, 7, 6, 2, 4, 4, 14, 3, 4, 2, 16, 4, 12, 9, 2, 5, 16, 2, 2, 3, 16, 6, 10, 4, 2, 4, 22, 2, 6, 3, 6, 10, 6, 3, 22, 5, 2, 3, 4, 2, 18, 4, 26, 10, 4, 5, 6, 2, 2, 7, 6, 2, 10, 5, 2, 9, 4, 2, 16, 3, 6, 9, 2, 3, 30, 5, 14, 6, 24, 5, 16, 5

Offset: 1

Author

Derek Orr, Mar 06 2014

Keywords

• nonn

Examples

			a(1) = 3 because for k = 1, 1*(1^3) - 1 = 0 is not prime, for k = 2, 2*(1^3) - 1 = 1 is not prime, but for k = 3, 3*(1^3) - 1 = 2 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A231819, A053989.

Programs

Mathematica

sk[n_]:=Module[{k=1,n3=n^3},While[!PrimeQ[k*n3-1],k++];k]; Array[sk,80] (* Harvey P. Dale, Jan 04 2023 *)

Python

import sympy
from sympy import isprime
def f(n):
  for k in range(1,10**3):
    if isprime(k*(n**3)-1):
      return k
n = 1
while n < 10**3:
  print(f(n))
  n += 1