A329941 - OEIS

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A329941

Least prime, p, such that 2*p*3^n - 1 and 2*p*3^n + 1 are twin primes.

2, 11, 2, 5, 43, 29, 53, 311, 113, 109, 367, 859, 647, 11, 2, 619, 13, 1051, 157, 2801, 3767, 5, 337, 1721, 3517, 41, 4013, 1879, 1873, 13649, 4637, 2909, 8387, 6521, 1453, 6599, 1277, 4801, 167, 1031, 11213, 4129, 4933, 199, 1427, 859, 9227, 5581, 863, 11959, 10453

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

2*2*3^1 - 1 = 11; 11 and 13 are twin primes so a(1)=2.

2*11*3^2 - 1 = 197; 197 and 199 are twin primes so a(2)=11 as no other prime p < 11 gives twin primes.

MATHEMATICA

Array[Block[{p = 2}, While[! AllTrue[2 p 3^# + {-1, 1}, PrimeQ], p = NextPrime@ p]; p] &, 51] (* Michael De Vlieger, Dec 24 2019 *)

PROG

(PARI) a(n) = {my(p=2); while (!isprime(2*p*3^n - 1) || !isprime(2*p*3^n + 1), p = nextprime(p+1)); p; } \\ Michel Marcus, Nov 25 2019