A109748 Integers n such that n is prime and x is prime, where (x,y) is the smallest solution to the Pell equation with D = n.

2, 3, 37, 73, 97, 577, 757, 997, 1297, 4357, 5197, 7213, 7873, 8737, 8761, 10273, 13033, 18097, 23041, 23593, 24169, 24337, 24697, 26713, 29437, 37117, 41257, 41617, 43117, 45817, 46573, 49033, 49201, 49393, 56857, 57601, 59341, 60601

Offset: 1

Author

Jonathan Vos Post, Aug 10 2005

Keywords

• nonn

Examples

			a(1) = 2 because 2 is prime, 3 is prime and (3,2) is the smallest x,y solution such that x^2 - 2*(y^2) = 1.
a(2) = 3 because 3 is prime, 2 is prime and (2,1) is the smallest x,y solution such that x^2 - 3*(y^2) = 1.
a(3) = 37 because 37 is prime, 73 is prime and (73,12) is the smallest x,y solution such that x^2 - 37*(y^2) = 1.
a(4) = 73 because 73 is prime, 2281249 is prime and (2281249,267000) is the smallest x,y solution such that x^2 - 73*(y^2) = 1.
a(5) = 97 because 97 is prime, 62809633 is prime and (62809633,6377352) is the smallest x,y solution such that x^2 - 97*(y^2) = 1.
		

References

• Beiler, A. H. "The Pellian." Ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. New York: Dover, pp. 248-268, 1966.
• Cohn, H. "Pell's Equation." Sect. 6.9 in Advanced Number Theory. New York: Dover, pp. 110-111, 1980.
• Cox, D. A. Primes of the form x^2 + ny^2. New York: Wiley, 1989.

Links

• Eric Weisstein's World of Mathematics, Pell Equation

Crossrefs

Cf. A062326 (for the case of n and y both prime).

Formula

n prime and x prime, where (x, y) is the smallest solution to the Pell equation x^2 - n*(y^2) = 1.

Extensions

More terms from T. D. Noe, May 17 2007