A237704 Numbers n for which the fundamental solution of Pell's equation x^2 - n*y^2 = 1 has both x and y prime.

2, 6, 12, 30, 32, 40, 42, 72, 90, 132, 152, 192, 210, 240, 312, 342, 408, 420, 462, 480, 552, 560, 592, 672, 702, 792, 870, 880, 888, 912, 930, 1122, 1152, 1260, 1272, 1320, 1332, 1560, 1584, 1722, 1752, 1792, 1980, 2352, 2520, 2550, 2652, 2712, 2862, 2952, 2970, 3192, 3560, 3640, 4032

Offset: 1

Author

Jani Melik, Feb 11 2014

Keywords

• nonn

Examples

			Pell's equation x^2 - 2*y^2 = 1 and its fundamental solution is (x,y) = (3,2) which are both primes, so a(1) = 2.
(x,y) = (5,2) satisfies x^2 - 6*y^2 = 1, so a(2) = 6.
(x,y) = (7,2) satisfies x^2 - 12*y^2 = 1, so a(3) = 12.
Pell's equation x^2 - 2088*y^2 = 1 and (x,y) = (19603, 429), 19603 is prime, 429 = 3 * 11 * 13 is not, so 2088 is not included.
Pell's equation x^2 - 2000*y^2 = 1 and (x,y) = (930249, 20801), 930249 = 3^2 * 41 * 2521 and 20801 = 11 * 31 * 61 are not primes, so 2000 is not included.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..716
• Wikipedia, Pell's equation

Crossrefs

Cf. A000037, A033313, A033317.

Extensions

420 inserted into the sequence by Colin Barker, Feb 12 2014