A254937 - OEIS

%I #7 Feb 24 2015 05:34:07

%S 7,9,11,15,19,13,17,19,27,31,21,19,29,37,21,31,25,23,43,29,25,45,49,

%T 29,35,27,39,43,41,35,33,53,61,35,47,33,51,55,59,63,43,53,41,39,61,37,

%U 73,55,43

%N Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A007519(n), n>=1 (primes congruent to 1 mod 8).

%C The corresponding positive fundamental solution x2(n) of this second class solutions is given in A254936(n).

%C See the comments and the Nagell reference in A254934.

%F A254936(n)^2 - 2*a(n)^2 = -A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.

%F a(n) = -(2*A254934(n) - 3*A254935(n)), n >= 1.

%e n = 2: 11^2 - 2*9^2 = 121 - 162 = -41.

%e a(2) = -(2*3 - 3*5) = 9.

%e See also A254936.

%Y Cf. A007519, A254936, A254934, A254935, A255234, A255248, A254760.

%K nonn,look,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 18 2015