A272057 Numbers n such that 3*4^n - 1 is prime.

1, 2, 3, 9, 17, 19, 32, 38, 47, 103, 108, 153, 162, 229, 235, 637, 1638, 2102, 2567, 6338, 7449, 12845, 20814, 40165, 61815, 77965, 117380, 207420, 351019, 496350, 600523, 1156367, 2117707, 5742009, 5865925, 5947859

Offset: 1

Author

Tim Johannes Ohrtmann, Apr 19 2016

Keywords

• nonn
• hard
• more

Comments

These are Williams primes to base 3.

Half of the even terms of A002235.

Links

• H. C. Williams, The primality of certain integers of the form 2Ar^n - 1, Acta Arith. 39 (1981), 7-17.

Crossrefs

Cf. A002235, A000043, A003307, A046865, A079906, A046866, A268061, A268356, A056725, A046867, A079907.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[3*4^# - 1] &]

PARI

for(n=1,10000, if(isprime(3*4^n-1), print1(n,", ")))

Extensions

a(25) corrected and a(33)-a(36) added by Giovanni Resta, Apr 19 2016, using data from A002235.