A238847 Smallest k such that k*n^3 + 1 is prime.

1, 2, 4, 3, 2, 2, 4, 15, 2, 3, 2, 2, 6, 3, 10, 3, 26, 3, 4, 2, 2, 15, 26, 7, 4, 2, 2, 6, 2, 2, 10, 2, 20, 4, 2, 3, 4, 3, 4, 6, 6, 4, 10, 2, 14, 16, 12, 3, 4, 9, 10, 6, 24, 3, 4, 6, 2, 3, 2, 2, 18, 6, 6, 3, 14, 5, 16, 9, 18, 3, 2, 2, 4, 3, 10, 6

Offset: 1

Author

Derek Orr, Mar 06 2014

Keywords

• nonn

Examples

			a(1) = 1 because in order for k*(1^3)+1 to be the smallest prime, k must be 1 (1*(1^3)+1 = 2).
a(2) = 2 because in order for k*(2^3)+1 to be the smallest prime, k must be 2 (2*(2^3)+1 = 17).
a(3) = 4 because in order for k*(3^3)+1 to be the smallest prime, k must be 4 (4*(3^3)+1 = 109).
		

Crossrefs

Cf. A034693, A035092.

Programs

Mathematica

sk[n_]:=Module[{k=1,n3=n^3},While[!PrimeQ[k*n3+1],k++];k]; Array[sk, 80] (* Harvey P. Dale, Aug 27 2014 *)
Table[SelectFirst[Range[10^2], PrimeQ[# n^3 + 1] &], {n, 76}] (* Michael De Vlieger, Mar 27 2016, Version 10 *)

PARI

a(n) = {k=1; while(!isprime(k*n^3+1), k++); k;} \\ Altug Alkan, Mar 26 2016

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