A216888 Numbers k such that 6*3^k + 1 is prime.

0, 1, 3, 4, 5, 8, 15, 16, 29, 53, 56, 59, 64, 131, 179, 319, 695, 781, 821, 896, 1251, 1453, 4216, 5479, 6224, 7841, 12095, 13781, 17719, 43955, 64821, 82779, 105105, 152528, 165895, 191813, 529679, 1074725, 1086111, 1175231, 1277861, 1346541, 3123035, 3648968, 5570080, 6236771, 10852676

Offset: 1

Author

Vincenzo Librandi, Sep 26 2012

Keywords

• nonn
• hard

Examples

			3 is a term because 6*3^3 + 1 = 163 is prime.
7 is not a term because 6*3^7 + 1 = 13123 = 11*1193 is composite.
		

Crossrefs

Cf. A003306, A005537, A005538, A005539; A056800, A056805, A143279.

Associated primes are in A111974.

Programs

Magma

/* Gives only the terms up to 1453: */ [n: n in [0..1500] | IsPrime(6*3^n + 1)];

Mathematica

Select[Range[5000], PrimeQ[6 3^# + 1] &]

PARI

is(n)=ispseudoprime(6*3^n+1) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = A003306(n+1)-1. - Bruno Berselli, Sep 27 2012

Extensions

More terms from Vincenzo Librandi, Oct 01 2012

a(41)-a(47) from the data at A003306 added by Amiram Eldar, Jul 18 2025