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

Offset: 1

Author

Pierre CAMI, Nov 24 2019

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A130327.

Programs

Mathematica

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

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