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Search: id:A163742
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| 7, 5, 41, 29, 63018038201, 44560482149, 19175002942688032928599, 13558774610046711780701
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OFFSET
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1,1
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COMMENT
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By construction, all these pairs fulfill 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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EXAMPLE
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(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
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Cf. A086397, A118612.
Sequence in context: A070426 A142883 A146382 this_sequence A089244 A063003 A038271
Adjacent sequences: A163739 A163740 A163741 this_sequence A163743 A163744 A163745
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KEYWORD
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nonn,less
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2009
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EXTENSIONS
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Definition clarified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 2009
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