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.

7, 23, 207367, 1902391, 167, 1511, 28031, 79, 3142977463, 2473230126937097422987916357409859838765327, 2499581669222318172005765848188928913768594409919797075052820591, 223

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