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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.

%I A109748 #10 Feb 16 2025 08:32:58
%S A109748 2,3,37,73,97,577,757,997,1297,4357,5197,7213,7873,8737,8761,10273,
%T A109748 13033,18097,23041,23593,24169,24337,24697,26713,29437,37117,41257,
%U A109748 41617,43117,45817,46573,49033,49201,49393,56857,57601,59341,60601
%N 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.
%D A109748 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.
%D A109748 Cohn, H. "Pell's Equation." Sect. 6.9 in Advanced Number Theory. New York: Dover, pp. 110-111, 1980.
%D A109748 Cox, D. A. Primes of the form x^2 + ny^2. New York: Wiley, 1989.
%H A109748 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>
%F A109748 n prime and x prime, where (x, y) is the smallest solution to the Pell equation x^2 - n*(y^2) = 1.
%e A109748 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.
%e A109748 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.
%e A109748 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.
%e A109748 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.
%e A109748 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.
%Y A109748 Cf. A062326 (for the case of n and y both prime).
%K A109748 nonn
%O A109748 1,1
%A A109748 _Jonathan Vos Post_, Aug 10 2005
%E A109748 More terms from _T. D. Noe_, May 17 2007