A239677 Least numbers k such that k*3^n-1 is prime.

1, 2, 2, 8, 4, 6, 2, 2, 16, 8, 6, 2, 16, 10, 4, 14, 8, 18, 6, 2, 18, 6, 2, 20, 18, 6, 2, 38, 30, 10, 16, 20, 18, 6, 2, 60, 20, 10, 10, 40, 58, 48, 16, 12, 4, 32, 90, 30, 10, 8, 130, 62, 26, 10, 6, 2, 30, 10, 32, 18, 6, 2, 74, 28, 46, 18, 6, 2, 30, 10, 46, 80, 94, 52

Offset: 1

Author

Derek Orr, Mar 23 2014

Keywords

• nonn

Comments

All the numbers in this sequence, excluding a(1), are even.

Examples

			1*3^2-1 = 8 is not prime. 2*3^2-1 = 17 is prime. Thus, a(2) = 2.
1*3^5-1 = 242 is not prime. 2*3^5-1 = 485 is not prime. 3*3^5-1 = 728 is not prime. 4*3^5-1 = 971 is prime. Thus, a(5) = 4.
		

Crossrefs

Cf. A085427.

Programs

PARI

for(n=1, 100, k=0; while(!isprime(k*3^n-1), k++); print1(k, ", ")) \\ Colin Barker, Mar 24 2014

Python

import sympy
from sympy import isprime
def Pow_3(n):
  for k in range(10**4):
    if isprime(k*(3**n)-1):
      return n
n = 1
while n < 100:
  print(Pow_3(n))
  n += 1