login
Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007519(n), n>=1 (primes congruent to 1 mod 8).
6

%I #9 Feb 24 2015 05:35:24

%S 3,5,7,7,7,9,9,11,11,11,13,15,13,13,17,15,17,19,15,17,21,17,17,21,19,

%T 23,19,19,21,23,25,21,21,27,23,29,23,23,23,23

%N Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007519(n), n>=1 (primes congruent to 1 mod 8).

%C For the corresponding term x1(n) see A254934(n).

%C See A254934 also for the Nagell reference.

%C The least positive y solutions (that is the ones of the first class) for the primes +1 and -1 (mod 8) together (including prime 2) are given in A255246.

%F A254934(n)^2 - 2*a(n)^2 = -A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

%e See A254934.

%e n = 3: 5^2 - 2*7^2 = 25 - 98 = 73.

%Y Cf. A007519, A254934, A254936, A254937, A254938, A255232.

%K nonn,look,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 18 2015