A124986 Primes of the form 12*k + 5 generated recursively. Initial prime is 5. General term is a(n) = Min_{p is prime; p divides 1 + 4*Q^2; p == 5 (mod 12)}, where Q is the product of previous terms in the sequence.

5, 101, 1020101, 53, 29, 2507707213238852620996901, 449, 433361, 401, 925177698346131180901394980203075088053316845914981, 44876921, 17, 173

Offset

1,1

Comments

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

At least one prime divisor of 1+4Q^2 is congruent to 2 modulo 3 and hence to 5 modulo 12.

The first seven terms are the same as those of A057207.

The next term is known but is too large to include.

Links

Robert Price, Table of n, a(n) for n = 1..14

Example

a(8) = 433361 is the smallest prime divisor congruent to 5 mod 12 of 1+4Q^2 = 3179238942812523869898723304484664524974766291591037769022962819805514576256901 = 13 * 433361 * 42408853 * 2272998442375593325550634821 * 5854291291251561948836681114631909089, where Q = 5 * 101 * 1020101 * 53 * 29 * 2507707213238852620996901 * 449.

Mathematica

a={5}; q=1;
For[n=2, n<=5, n++,
    q=q*Last[a];
    AppendTo[a, Min[Select[FactorInteger[4*q^2+1][[All, 1]], Mod[#, 12]==5 &]]];
    ];
a (* Robert Price, Jul 16 2015 *)

Crossrefs

Cf. A000945, A040117, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Sequence in context: A337828 A275749 A057207 * A231830 A260024 A123626

Adjacent sequences: A124983 A124984 A124985 * A124987 A124988 A124989

Keyword

nonn

Author

Nick Hobson, Nov 18 2006 and Nov 23 2006

Status

approved