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A294091
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Numbers k such that (k - 1)/2 is prime that are not congruent to -1 mod 8.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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).
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REFERENCES
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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.
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LINKS
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MAPLE
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map(t->2*t+1, select(isprime, [2, seq(4*k+1, k=1..1000)])); # Robert Israel, Feb 27 2018
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MATHEMATICA
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Select[2*Prime@Range[109] + 1, ! Mod[#, 8] == 7 &]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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