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A363798
Numbers k such that there is no prime p for which p^k + 2*k is prime.
1
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.
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
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 23 2023
STATUS
approved