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

1,1

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

Crossrefs

Cf. A130327.

Sequence in context: A298444 A224480 A037299 * A347121 A341512 A276676

Adjacent sequences: A329938 A329939 A329940 * A329942 A329943 A329944

Keyword

nonn

Author

Pierre CAMI, Nov 24 2019

Status

approved