cp's OEIS Frontend

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.

%I A124986 #13 Aug 06 2022 08:18:37
%S A124986 5,101,1020101,53,29,2507707213238852620996901,449,433361,401,
%T A124986 925177698346131180901394980203075088053316845914981,44876921,17,173
%N 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.
%C A124986 All prime divisors of 1+4Q^2 are congruent to 1 modulo 4.
%C A124986 At least one prime divisor of 1+4Q^2 is congruent to 2 modulo 3 and hence to 5 modulo 12.
%C A124986 The first seven terms are the same as those of A057207.
%C A124986 The next term is known but is too large to include.
%H A124986 Robert Price, <a href="/A124986/b124986.txt">Table of n, a(n) for n = 1..14</a>
%e A124986 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.
%t A124986 a={5}; q=1;
%t A124986 For[n=2,n<=5,n++,
%t A124986     q=q*Last[a];
%t A124986     AppendTo[a,Min[Select[FactorInteger[4*q^2+1][[All,1]],Mod[#,12]==5 &]]];
%t A124986     ];
%t A124986 a (* _Robert Price_, Jul 16 2015 *)
%Y A124986 Cf. A000945, A040117, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A124986 nonn
%O A124986 1,1
%A A124986 _Nick Hobson_, Nov 18 2006 and Nov 23 2006