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A163742
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Prime pairs (p,q) of the form p=A002315(k), q=A001653(k) for some k.
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OFFSET
| 1,1
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COMMENTS
| By construction, all these pairs fulfil p^2 -2*q^2 = -1.
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.
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LINKS
| V. Librandi, Pell's equation with prime solutions
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EXAMPLE
| (A002315(1),A001653(1)) = (7,5) are both prime and define the first pair in the sequence.
(A002315(2),A001653(2)) = (41,29) are both prime and define the second pair in the sequence.
(A002315(3),A001653(3)) = (239,169=13^2) contain the composite 169 and do not contribute to the sequence.
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CROSSREFS
| Cf. A086397, A118612.
Sequence in context: A070426 A142883 A146382 * A202130 A089244 A063003
Adjacent sequences: A163739 A163740 A163741 * A163743 A163744 A163745
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KEYWORD
| nonn,less
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2009
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EXTENSIONS
| Definition clarified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 2009
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