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A254936 Fundamental positive solution x = x2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A007519(n), n >= 1 (primes congruent to 1 mod 8). 5
9, 11, 13, 19, 25, 15, 21, 23, 35, 41, 25, 21, 37, 49, 23, 39, 29, 25, 57, 35, 27, 59, 65, 33, 43, 29, 49, 55, 51, 41, 37, 69, 81, 39, 59, 35, 65, 71, 77, 83, 51, 67, 47, 43, 79, 39, 97, 69, 49, 59 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The corresponding term y = y2(n) of this fundamental solution of the second class of the (generalized) Pell equation x^2 - 2*y^2 = -A007519(n) = -(1 + 8*A005123(n)) is given in A254937(n).

For comments and the Nagell reference see A254934.

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(n)^2 - 2*A254937(n)^2 = -A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.

a(n) = -(3*A254934(n) - 4*A254935(n)), n >= 1.

EXAMPLE

The first pairs [x2(n), y2(n)] of the fundamental positive solutions of this second class are (the prime A007519(n) appears as first entry):

[17, [9, 7]], [41, [11, 9]], [73, [13, 11]],

[89, [19, 15]], [97, [25, 19]], [113, [15, 13]],

[137, [21, 17]], [193, [23, 19]], [233, [35, 27]],

[241, [41, 31]], [257, [25, 21]], [281, [21, 19]],

[313, [37, 29]], [337, [49, 37]], [353, [23, 21]],

[401, [39, 31]], [409, [29, 25]], [433, [25, 23]],

[449, [57, 43]], [457, [35, 29]], [521, [27, 25]],

[569, [59, 45]], [577, [65, 49]], [593, [33, 29]],

[601, [43, 35]], [617, [29, 27]], [641, [49, 39]], ...

a(4) = -(3*3 - 4*7) = 28 - 9 = 19.

CROSSREFS

Cf. A007519, A005123, A254937, A254934, A254935, A255233, A255247.

Sequence in context: A291350 A289697 A104296 * A117675 A027726 A044873

Adjacent sequences:  A254933 A254934 A254935 * A254937 A254938 A254939

KEYWORD

nonn,look,easy

AUTHOR

Wolfdieter Lang, Feb 18 2015

STATUS

approved

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Last modified November 14 00:05 EST 2019. Contains 329106 sequences. (Running on oeis4.)