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A057205 Primes congruent to 3 modulo 4 generated recursively: a(n) = Min_{p, prime; p mod 4 = 3; p|4Q-1}, where Q is the product of all previous terms in the sequence. The initial term is 3.

%I A057205 #16 Dec 12 2021 20:00:33
%S A057205 3,11,131,17291,298995971,8779,594359,59,151,983,19,
%T A057205 38851089348584904271503421339,
%U A057205 2359886893253830912337243172544609142020402559023,823818731,2287,7,9680188101680097499940803368598534875039120224550520256994576755856639426217960921548886589841784188388581120523,163,83,1471,34211,2350509754734287,23567
%N A057205 Primes congruent to 3 modulo 4 generated recursively: a(n) = Min_{p, prime; p mod 4 = 3; p|4Q-1}, where Q is the product of all previous terms in the sequence. The initial term is 3.
%D A057205 P. G. L. Dirichlet (1871): Vorlesungen uber Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages.
%D A057205 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 13.
%e A057205 a(4) = 17291 = 4*4322 + 3 is the smallest prime divisor congruent to 3 (mod 4) of Q = 3*11*131 - 1 = 17291.
%t A057205 a={3}; q=1;
%t A057205 For[n=2,n<=7,n++,
%t A057205     q=q*Last[a];
%t A057205     AppendTo[a,Min[Select[FactorInteger[4*q-1][[All,1]],Mod[#,4]==3&]]];
%t A057205     ];
%t A057205 a (* _Robert Price_, Jul 18 2015 *)
%Y A057205 Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002476, A057204-A057208.
%K A057205 nonn
%O A057205 1,1
%A A057205 _Labos Elemer_, Oct 09 2000
%E A057205 More terms from _Phil Carmody_, Sep 18 2005
%E A057205 Terms corrected and extended by _Sean A. Irvine_, Oct 23 2014