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A255246 Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A038873(n), n>=1 (primes congruent to {1,2,7} mod 8). 5

%I #13 Feb 26 2015 04:01:38

%S 3,2,3,4,4,5,6,6,7,8,7,7,8,9,8,9,10,12,10,11,10,14,11,12,11,13,12,14,

%T 15,14,13,13,17,18,14,14,15,17,16,19,20,15,17,16,18,16,16,21,17,17,21,

%U 18,19,22,23,20,19,18,19,20,26,22,20,21,23,25,26,28,21

%N Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A038873(n), n>=1 (primes congruent to {1,2,7} mod 8).

%C For the corresponding term x1(n) see A255235(n).

%C For the primes 1 (mod 8) see A154935, and for the primes 7 (mod 8) see 2*A255232.

%C See A254934 and A254938 also for the derivation based on the Nagell reference given there.

%F A255235(n)^2 - 2*a(n)^2 = -A038873(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

%e See A255235.

%e n = 1: 4^2 - 2*3^2 = -2 = -A038873(1),

%e n = 3: 1^2 - 2*3^2 = 1 - 18 = -17 = -A038873(3).

%Y Cf. A038873, A255235, A255247, A255248, A254935, 2*A255232, A002335.

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 25 2015

%E More terms from _Colin Barker_, Feb 26 2015

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Last modified April 19 09:23 EDT 2024. Contains 371782 sequences. (Running on oeis4.)