A390050 Numbers k such that 256 * 3^k - 1 is prime.

3, 5, 15, 35, 41, 105, 203, 213, 753, 1677, 2231, 4317, 6065, 6587

Offset

1,1

Comments

a(15) > 300000. All values of this sequence must be odd numbers because an even k would produce 256 * 3^k - 1 that is the difference of two squares, so not prime for any such difference > 4. This sequence has an empty intersection set with A390051 so no twin primes have a center (average) at 2^8 * 3^k. A covering system can be constructed that demonstrates this (see attached link).

Links

Table of n, a(n) for n=1..14.

Ken Clements, Python program to calculate covering system.

Mathematica

Select[Range[0, 3000], PrimeQ[256 * 3^# - 1] &] (* Amiram Eldar, Oct 24 2025 *)

Prog

(Python)
from gmpy2 import is_prime
print([ k for k in range(4000) if is_prime(256 * 3**k - 1, 50)])

Crossrefs

Cf. A027856, A003307, A005540, A005541, A385115, A387197, A387760, A384228, A390051.

Sequence in context: A148501 A148502 A295614 * A089485 A279684 A146212

Adjacent sequences: A390047 A390048 A390049 * A390051 A390052 A390053

Keyword

nonn,more

Author

Ken Clements, Oct 22 2025

Status

approved