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

Author

Arkadiusz Wesolowski, Feb 09 2018

Keywords

• nonn
• easy

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

Crossrefs

Cf. A005385. A269454 gives the primes.

Programs

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 &]