A239676 Least k such that k*3^n+1 is prime.

1, 2, 2, 4, 2, 2, 2, 8, 6, 2, 8, 28, 10, 12, 4, 4, 2, 2, 10, 20, 26, 24, 8, 48, 16, 34, 14, 14, 18, 6, 2, 26, 26, 14, 22, 26, 16, 22, 12, 4, 62, 64, 68, 88, 70, 56, 34, 96, 32, 50, 20, 24, 8, 6, 2, 18, 6, 2, 8, 6, 2, 42, 14, 18, 6, 2, 98, 66, 22, 70, 74, 80, 68, 52

Offset: 0

Author

Derek Orr, Mar 23 2014

Keywords

• nonn

Comments

All numbers in this sequence, except for a(0), are even.

Examples

			1*3^1+1 = 4 is not prime. 2*3^1+1 = 7 is prime. Thus, a(1) = 2.
1*3^3+1 = 28 is not prime. 2*3^3+1 = 57 is not prime. 3*3^3+1 = 82 is not prime. 4*3^3+1 = 109 is prime. Thus, a(3) = 4.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A003306 (where k=2), A035050 (k*2^n+1 is prime).

Programs

Magma

sol:=[];m:=1; for n in [0..73] do k:=0; while not IsPrime(k*3^n+1) do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // Marius A. Burtea, Jun 05 2019

Mathematica

lk[n_]:=Module[{k=1,t=3^n},While[!PrimeQ[k*t+1],k++];k]; Array[lk,80,0] (* Harvey P. Dale, May 11 2025 *)

PARI

for(n=0, 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 Pow3(n):
  for k in range(10**4):
    if isprime(k*(3**n)+1):
      return n
n = 1
while n < 100:
  print(Pow3(n))
  n += 1