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A294091
Numbers k such that (k - 1)/2 is prime that are not congruent to -1 mod 8.
1
5, 11, 27, 35, 59, 75, 83, 107, 123, 147, 179, 195, 203, 219, 227, 275, 299, 315, 347, 363, 387, 395, 459, 467, 483, 515, 539, 555, 563, 587, 627, 635, 675, 699, 707, 747, 779, 795, 803, 819, 843, 867, 899, 915, 923, 1019, 1043, 1083, 1115, 1139, 1155, 1187
OFFSET
1,1
COMMENTS
k is prime if and only if 2^(k - 1) is congruent to 1 mod k. The test relies on the Selfridge criterion (see p. 42 of the Krizek et al. reference).
REFERENCES
M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, p. 42.
P. Ribenboim, The Little Book of Bigger Primes, Springer Science & Business Media, 2013, pp. 32-33.
LINKS
MAPLE
map(t->2*t+1, select(isprime, [2, seq(4*k+1, k=1..1000)])); # Robert Israel, Feb 27 2018
MATHEMATICA
Select[2*Prime@Range[109] + 1, ! Mod[#, 8] == 7 &]
CROSSREFS
Cf. A005385. A269454 gives the primes.
Sequence in context: A372918 A274681 A287350 * A032379 A152535 A042423
KEYWORD
nonn,easy
AUTHOR
STATUS
approved