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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.

%I A124987 #21 Feb 13 2024 11:34:23
%S A124987 5,29,17,6076229,1289,78067083126343039013,521,8606045503613,15837917,
%T A124987 1873731749,809,137,2237,17729
%N 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.
%C A124987 Since Q is odd, all prime divisors of 4+Q^2 are congruent to 1 modulo 4.
%C A124987 At least one prime divisor of 4+Q^2 is congruent to 2 modulo 3 and hence to 5 modulo 12.
%C A124987 The first two terms are the same as those of A057208.
%H A124987 Tyler Busby, <a href="/A124987/b124987.txt">Table of n, a(n) for n = 1..15</a>
%e A124987 a(3) = 17 is the smallest prime divisor congruent to 5 mod 12 of 4+Q^2 = 21029 = 17 * 1237, where Q = 5 * 29.
%t A124987 a={5}; q=1;
%t A124987 For[n=2,n<=5,n++,
%t A124987     q=q*Last[a];
%t A124987     AppendTo[a,Min[Select[FactorInteger[q^2+4][[All,1]],Mod[#,12]==5 &]]];
%t A124987     ];
%t A124987 a (* _Robert Price_, Jul 16 2015 *)
%Y A124987 Cf. A000945, A040117, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A124987 more,nonn
%O A124987 1,1
%A A124987 _Nick Hobson_, Nov 18 2006