A363798 Numbers k such that there is no prime p for which p^k + 2*k is prime.

12, 16, 22, 24, 28, 32, 40, 46, 52, 58, 60, 64, 66, 70, 72, 76, 82, 84, 88, 92, 94, 100, 106, 108, 112, 118, 124, 130, 132, 136, 142, 144, 148, 150, 152, 154, 166, 170, 172, 178, 180, 184, 190, 192, 196, 202, 208, 212, 214, 220, 226, 232, 234, 238, 240, 244, 250, 252, 256, 262, 264, 268, 272, 274

Offset

1,1

Comments

Numbers k such that A363796(k) = -1.

Includes k = (q^2-1)/2 + j*(q^2-q) for odd primes q and nonnegative integers j such that q^k + 2*k is not prime, since for primes p <> q we have q | p^k + 2*k. Conjecture: all terms are of this form.

Links

Table of n, a(n) for n=1..64.

Example

a(3) = 22 is a term because 3 | p^22 + 2*22 for all primes p <> 3, while 3^22 + 2*22 = 31381059653 = 59 * 2447 * 217361 is not prime.

Maple

# Run Maple program for A363796. Then:
select(k -> V[k]=-1, [$1..400]);

Crossrefs

Cf. A363796.

Sequence in context: A183052 A344079 A240052 * A070329 A064695 A162824

Adjacent sequences: A363795 A363796 A363797 * A363799 A363800 A363801

Keyword

nonn

Author

Robert Israel, Jun 23 2023

Status

approved