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%I #14 May 30 2013 13:12:09
%S 7,5,41,29,63018038201,44560482149,19175002942688032928599,
%T 13558774610046711780701
%N Prime pairs (p,q) of the form p=A002315(k), q=A001653(k) for some k.
%C By construction, all these pairs satisfy p^2 -2*q^2 = -1.
%C One can generate the combined A002315 and A001653 by a mixed recursion 3p+4q -> p; 2p+3q -> q, and then test after each step both p and q for primality.
%H V. Librandi, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&threadID=566075&messageID=1689564#1689564">Pell's equation with prime solutions</a>
%e (A002315(1),A001653(1)) = (7,5) are both prime and define the first pair in the sequence.
%e (A002315(2),A001653(2)) = (41,29) are both prime and define the second pair in the sequence.
%e (A002315(3),A001653(3)) = (239,169=13^2) contain the composite 169 and do not contribute to the sequence.
%Y Cf. A086397, A118612.
%K nonn,less
%O 1,1
%A _Vincenzo Librandi_, Aug 03 2009
%E Definition clarified by _R. J. Mathar_, Aug 12 2009
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