A124987 Primes of the form 12k+5 generated recursively. Initial prime is 5. General term is a(n) = Min {p is prime; p divides 4+Q^2; p == 5 (mod 12)}, where Q is the product of previous terms in the sequence.

5, 29, 17, 6076229, 1289, 78067083126343039013, 521, 8606045503613, 15837917, 1873731749, 809, 137, 2237, 17729

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• more
• nonn

Comments

Since Q is odd, all prime divisors of 4+Q^2 are congruent to 1 modulo 4.

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

The first two terms are the same as those of A057208.

Examples

			a(3) = 17 is the smallest prime divisor congruent to 5 mod 12 of 4+Q^2 = 21029 = 17 * 1237, where Q = 5 * 29.
		

Links

• Tyler Busby, Table of n, a(n) for n = 1..15

Crossrefs

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

Programs

Mathematica

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