A124988 Primes of the form 12k+7 generated recursively. Initial prime is 7. General term is a(n)=Min {p is prime; p divides 3+4Q^2; Mod[p,12]=7}, where Q is the product of previous terms in the sequence.

7, 199, 7761799, 487, 67, 103, 1482549740515442455520791, 31, 139, 787, 19, 39266047, 1955959, 50650885759, 367, 185767, 62168707

Offset

1,1

Comments

All prime divisors of 3+4Q^2 are congruent to 1 modulo 6.

At least one prime divisor of 3+4Q^2 is congruent to 3 modulo 4 and hence to 7 modulo 12.

The first six terms are the same as those of A057204.

Links

Tyler Busby, Table of n, a(n) for n = 1..21

Example

a(3) = 1482549740515442455520791 is the smallest prime divisor congruent to 7 mod 12 of 3+4Q^2 = 5281642303363312989311974746340327 = 3562539697 * 1482549740515442455520791, where Q = 7 * 199 * 7761799 * 487 * 67 * 103.

Mathematica

a={7}; q=1;
For[n=2, n<=7, n++,
    q=q*Last[a];
    AppendTo[a, Min[Select[FactorInteger[4*q^2+3][[All, 1]], Mod[#, 12]==7 &]]];
    ];
a (* Robert Price, Jul 15 2015 *)

Crossrefs

Cf. A000945, A068229, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Sequence in context: A202943 A355088 A057204 * A220934 A221288 A355087

Adjacent sequences: A124985 A124986 A124987 * A124989 A124990 A124991

Keyword

nonn

Author

Nick Hobson, Nov 18 2006

Status

approved