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A163742 Prime pairs (p,q) of the form p=A002315(k), q=A001653(k) for some k. 1
7, 5, 41, 29, 63018038201, 44560482149, 19175002942688032928599, 13558774610046711780701 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..8.

V. Librandi, Pell's equation with prime solutions

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.

CROSSREFS

Cf. A086397, A118612.

Sequence in context: A341431 A142883 A146382 * A202130 A089244 A063003

Adjacent sequences:  A163739 A163740 A163741 * A163743 A163744 A163745

KEYWORD

nonn,less

AUTHOR

Vincenzo Librandi, Aug 03 2009

EXTENSIONS

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

STATUS

approved

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)