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A255248 Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A001132(n), n>=1 (primes congruent to {1,7} mod 8) 4

%I #8 Feb 26 2015 04:00:59

%S 4,7,6,10,9,8,16,11,10,15,19,14,13,22,17,16,14,24,19,28,16,27,22,31,

%T 21,26,20,19,24,29,37,21,20,32,36,31,25,30,23,22,43,29,34,28,38,42,25,

%U 45,49,29,40,35,28,27,34,39,52,43,42,28,36,46,41,35,33,32

%N Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A001132(n), n>=1 (primes congruent to {1,7} mod 8)

%C For the corresponding term x2(n) see A255247(n).

%C See the comments on A255247.

%F A255247(n)^2 - 2*a(n)^2 = -A001132(n), n >= 1, gives the second smallest positive (proper) solution of this (generalized) Pell equation.

%F a(n) = -(2*A255235(n+1) - 3*A255246(n+1)), n >= 1.

%e See A255247.

%e a(4) = -(2*1 - 3*4) = 12 - 2 = 10.

%e n=4: 13^2 - 2*10^2 = 169 - 200 = -31 = -A001132(4).

%Y Cf. A001132, A255247, A255235, A255246, A254937, A255234, A254931.

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 19 2015

%E More terms from _Colin Barker_, Feb 26 2015

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