A385115 Numbers k such that 2^4 * 3^k - 1 is prime.

1, 3, 9, 13, 31, 43, 81, 121, 235, 1135, 1245, 1521, 2019, 2329, 3573, 11245, 15571, 37333, 54471, 70641

Offset: 1

Author

Ken Clements, Aug 14 2025

Keywords

• nonn
• more

Comments

All terms are odd, since if k were even, N = 2^4 * 3^k would be a perfect square and N - 1 could be factored as the difference of squares, hence not prime.

a(21) > 10^5. - Michael S. Branicky, Aug 15 2025

Crossrefs

Cf. A005540, A005541, A387060.

Programs

Mathematica

Select[Range[4000], PrimeQ[16 * 3^# - 1] &] (* Amiram Eldar, Aug 15 2025 *)

Python

from gmpy2 import is_prime
print([k for k in range(1, 4_000, 2) if is_prime(16 * 3**k - 1)])

Extensions

a(17)-a(20) from Michael S. Branicky, Aug 15 2025