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A390051

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

0, 1, 9, 27, 36, 37, 44, 45, 48, 55, 60, 68, 76, 172, 199, 224, 320, 343, 404, 487, 628, 756, 829, 1059, 1268, 1740, 2260, 3076, 3163, 3295, 3981, 5772, 8624, 12925, 13339, 14691, 24237, 62768, 69171, 82333, 98563, 107841, 110688, 150645, 152548, 164052, 242905, 271423

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OFFSET

1,3

COMMENTS

a(49) > 300000. This sequence has an empty intersection set with A390050 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..48.

Ken Clements, Python program to calculate covering system.

MATHEMATICA

Select[Range[0, 4000], 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(128 * 3**k + 1, 50)])

CROSSREFS

Cf. A027856, A003306, A005537, A005538, A387060, A387201, A387761, A388408, A390050.

Sequence in context: A216168 A036303 A391243 * A359030 A325299 A353238