This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A163742 #18 Oct 22 2024 08:07:10 %S A163742 7,5,41,29,63018038201,44560482149,19175002942688032928599, %T A163742 13558774610046711780701 %N A163742 Prime pairs (p,q) of the form p=A002315(k), q=A001653(k) for some k. %C A163742 By construction, all these pairs satisfy p^2 -2*q^2 = -1. %C A163742 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 A163742 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 A163742 (A002315(1),A001653(1)) = (7,5) are both prime and define the first pair in the sequence. %e A163742 (A002315(2),A001653(2)) = (41,29) are both prime and define the second pair in the sequence. %e A163742 (A002315(3),A001653(3)) = (239,169=13^2) contain the composite 169 and do not contribute to the sequence. %Y A163742 Bisections are (essentially): A086397, A118612. %K A163742 nonn,more %O A163742 1,1 %A A163742 _Vincenzo Librandi_, Aug 03 2009 %E A163742 Definition clarified by _R. J. Mathar_, Aug 12 2009