A254766
Fundamental positive solution x = x2(n) of the second class of the Pell equation x^2 - 2*y^2 = A007522(n), n >=1 (primes congruent to 7 mod 8).
Original entry on oeis.org
5, 11, 9, 17, 13, 23, 21, 17, 27, 35, 23, 21, 41, 31, 29, 39, 37, 53, 33, 31, 41, 59, 39, 49, 37, 35, 43, 63, 53, 37, 49, 77, 59, 47, 75, 83, 65, 53, 73, 51, 45, 61, 71, 59, 79, 69, 95, 55, 49, 101
Offset: 1
The first pairs [x2(n), y2(n)] of the fundamental positive solutions of the second class are (we list the prime A007522(n) as first entry): [7,[5,3]], [23,[11,7]], [31,[9,5]], [47,[17,11]], [71,[13,7]], [79,[23,15]], [103,[21,13]], [127,[17,9]], [151,[27,17]], [167,[35,23]], [191,[23,13]], [199,[21,11]], [223,[41,27]], [239,[31,19]], [263,[29,17]], [271,[39,25]], ...
A254929
Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = A007522(n), n>=1 (primes congruent to 7 mod 8).
Original entry on oeis.org
3, 7, 5, 11, 7, 15, 13, 9, 17, 23, 13, 11, 27, 19, 17, 25, 23, 35, 19, 17, 25, 39, 23, 31, 21, 19, 25, 41, 33, 19, 29, 51, 37, 27, 49, 55, 41, 31, 47, 29, 23, 37, 45, 35, 51, 43, 63, 31, 25, 67
Offset: 1
n = 2: 11^2 - 2*7^2 = 121 - 98 = 23.
The smallest positive solution is (x1(2), y1(2)) = (5, 1) from (A254764(2), A254765(2)).
See also A254766.
a(4) = 2*7 - 3*1 = 11.
A254765
Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = A007522(n), n >=1 (primes congruent to 7 mod 8).
Original entry on oeis.org
1, 1, 3, 1, 5, 1, 3, 7, 3, 1, 7, 9, 1, 5, 7, 3, 5, 1, 9, 11, 7, 1, 9, 5, 11, 13, 11, 3, 7, 17, 11, 1, 7, 13, 3, 1, 7, 13, 5, 15, 21, 11, 7, 13, 5, 9, 1, 17, 23, 1
Offset: 1
A254764(4)^2 - 2*a(4)^2 = 7^2 - 2*1^2 = 47 = A007522(4).
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