A163742 Prime pairs (p,q) of the form p=A002315(k), q=A001653(k) for some k.

7, 5, 41, 29, 63018038201, 44560482149, 19175002942688032928599, 13558774610046711780701

Offset: 1

Author

Vincenzo Librandi, Aug 03 2009

Keywords

• nonn
• more

Comments

By construction, all these pairs satisfy 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.

Examples

			(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.
		

Links

• V. Librandi, Pell's equation with prime solutions

Crossrefs

Bisections are (essentially): A086397, A118612.

Extensions

Definition clarified by R. J. Mathar, Aug 12 2009