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A254761 One half of the 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). 7

%I #10 Feb 18 2015 07:04:55

%S 1,1,1,2,3,1,2,2,4,5,2,1,4,6,1,4,2,1,7,3,1,7,8,2,4,1,5,6,5,3,2,8,10,2,

%T 6,1,7,8,9,10,4,7,3,2,9,1,12,7,3,5

%N One half of the 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 A254760(n).

%C See A254760 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 in the first class also prime 2) are given in A002335.

%F A254760(n)^2 - 2*(2*a(n))^2 = A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

%e See A254760.

%e n = 3: 9^2 - 2*(2*1)^2 = 81 - 8 = 73.

%Y Cf. A007519, A254760, A254762, 2*A254763, A002335.

%K nonn,easy

%O 1,4

%A _Wolfdieter Lang_, Feb 12 2015

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