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 A124985 Primes of the form 8*k + 7 generated recursively. Initial prime is 7. General term is a(n) = Min_{p is prime; p divides 8*Q^2 - 1; p == 7 (mod 8)}, where Q is the product of the previous terms. 0
 7, 23, 207367, 1902391, 167, 1511, 28031, 79, 3142977463, 2473230126937097422987916357409859838765327, 2499581669222318172005765848188928913768594409919797075052820591, 223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 8*Q^2 - 1 always has a prime divisor congruent to 7 modulo 8. REFERENCES D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 182. LINKS Table of n, a(n) for n=1..12. EXAMPLE a(4) = 1902391 is the smallest prime divisor, congruent to 7 modulo 8, of 8*Q^2 - 1 = 8917046441372551 = 97 * 1902391 * 48322513, where Q = 7 * 23 * 207367. MATHEMATICA a={7}; q=1; For[n=2, n<=9, n++, q=q*Last[a]; AppendTo[a, Min[Select[FactorInteger[8*q^2-1][[All, 1]], Mod[#, 8]==7&]]]; ]; a (* Robert Price, Jul 18 2015 *) PROG (PARI) main(size)={my(v=vector(size), i, q=1, t); for(i=1, size, t=1; while(!(prime(t)%8==7&&(8*q^2-1)%prime(t)==0), t++); v[i]=prime(t); q*=v[i]); v; } /* Anders Hellström, Jul 18 2015 */ CROSSREFS Cf. A000945, A007522, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045. Sequence in context: A009047 A129662 A012482 * A349078 A126612 A196113 Adjacent sequences: A124982 A124983 A124984 * A124986 A124987 A124988 KEYWORD nonn AUTHOR Nick Hobson, Nov 18 2006 EXTENSIONS Edited and added a(11)-a(12) by Max Alekseyev, May 31 2013 STATUS approved

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Last modified March 1 18:30 EST 2024. Contains 370443 sequences. (Running on oeis4.)