cp's OEIS Frontend

A217759 Primes of the form 4k+3 generated recursively: a(1)=3, a(n)= Min{p; p is prime; Mod[p,4]=3; p|4Q^2-1}, where Q is the product of all previous terms in the sequence.

%I A217759 #36 May 16 2013 14:13:14
%S A217759 3,7,43,19,6863,883,23,191,2927,205677423255820459,11,163,227,9127,59,
%T A217759 31,71,131627,2101324929412613521964366263134760336303,127,1302443,
%U A217759 4065403,107,2591,21487,223,12823,167,53720906651,5452254637117019,39827899,11719,131
%N A217759 Primes of the form 4k+3 generated recursively: a(1)=3, a(n)= Min{p; p is prime; Mod[p,4]=3; p|4Q^2-1}, where Q is the product of all previous terms in the sequence.
%C A217759 Contrast A057207, where all the factors are congruent to 1 (mod 4), here only one is guaranteed to be congruent to 3 (mod 4).
%D A217759 Dirichlet,P.G.L (1871): Vorlesungen uber Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages.
%D A217759 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 13.
%H A217759 Daran Gill, <a href="/A217759/b217759.txt">Table of n, a(n) for n = 1..51</a>
%H A217759 Mersenne Forum, <a href="http://mersenneforum.org/showthread.php?t=18015">Two new sequences</a>
%e A217759 a(10) is 205677423255820459 because it is the only prime factor congruent to 3 (mod 4) of 4*(3*7*43*19*6863*883*23*191*2927)^2-1 = 5*13*2088217*256085119729*205677423255820459. The four smaller factors are all congruent to 1 (mod 4).
%Y A217759 Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002145, A057204-A057208.
%K A217759 nonn
%O A217759 1,1
%A A217759 _Daran Gill_, Mar 23 2013