%I #22 Nov 12 2019 11:33:17
%S 555383,1767407,2103107,7400567,12836987,14668163,15404867,16238303,
%T 19572647,25003799,26978663,27370727,35182919,36180527,38553023,
%U 39714083,52503587,53061143,53735699,55072427,63302159,70728839,77199743,77401679,86334299,97298759,97375319
%N Primes q = 2*p+1 for which there are primes b < c < p such that b^p == c^p == 1 (mod q^2).
%C From D. Broadhurst, Oct 05 2011: (Start)
%C (p,q) is a Sophie Germain prime pair; (b,q) and (c,q) are Wieferich prime pairs; each of (b,c) is a square modulo q^2.
%C The sequence is now complete up to the 51st term, q=199065467.
%C It is a subsequence of A196511, where the latter does not require that q=2*p+1, is complete only up q=27370727, and contains q=2452757 and q=22796069, with q=4*p+1, (cf. link to post on "primenumbers" group), found by a simple analysis of Mossinghoff's results on Wieferich primes (cf. link).
%C With thanks to Mike Oakes. (End)
%H D. J. Broadhurst, <a href="/A196733/b196733.txt">Table of n, a(n) for n = 1..51</a>
%H D. J. Broadhurst et al., <a href="http://groups.yahoo.com/group/primenumbers/message/23175">Re: Square factors of b^p-1</a> on yahoo group "primenumbers", Sept.-Oct. 2011
%H David Broadhurst and others, <a href="/A196511/a196511.txt">Square factors of b^p-1</a>, digest of 81 messages in primenumbers Yahoo group, Sep 22 - Nov 29, 2011.
%H Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/WieferichBarker">Wieferich Prime Pairs, Barker Sequences, and Circulant Hadamard Matrices</a>, as of Feb 12 2009.
%Y Cf. A005384, A005385, A124121, A124122, A196511.
%K nonn
%O 1,1
%A _M. F. Hasler_, Oct 05 2011