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