A294091 Numbers k such that (k - 1)/2 is prime that are not congruent to -1 mod 8.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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: A038253 A274681 A287350 * A032379 A152535 A042423

Adjacent sequences: A294088 A294089 A294090 * A294092 A294093 A294094

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Feb 09 2018

Status

approved