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A237704
Numbers n for which the fundamental solution of Pell's equation x^2 - n*y^2 = 1 has both x and y prime.
1
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
1,1
LINKS
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jani Melik, Feb 11 2014
EXTENSIONS
420 inserted into the sequence by Colin Barker, Feb 12 2014
STATUS
approved