

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.


1



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
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OFFSET

1,1


REFERENCES

Beiler, A. H. "The Pellian." Ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. New York: Dover, pp. 248268, 1966.
Cohn, H. "Pell's Equation." Sect. 6.9 in Advanced Number Theory. New York: Dover, pp. 110111, 1980.
Cox, D. A. Primes of the form x^2 + ny^2. New York: Wiley, 1989.


LINKS

Table of n, a(n) for n=1..38.
Eric Weisstein's World of Mathematics, Pell Equation


FORMULA

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


EXAMPLE

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.


CROSSREFS

Cf. A062326 (for the case of n and y both prime).
Sequence in context: A266758 A280539 A216145 * A062459 A258455 A118370
Adjacent sequences: A109745 A109746 A109747 * A109749 A109750 A109751


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Aug 10 2005


EXTENSIONS

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


STATUS

approved



