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A255232 One half of the fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007522(n), n >= 1 (primes congruent to 7 mod 8). 8
1, 2, 2, 3, 3, 4, 4, 4, 5, 6, 5, 5, 7, 6, 6, 7, 7, 9, 7, 7, 8, 10, 8, 9, 8, 8, 9, 11, 10, 9, 10, 13, 11, 10, 13, 14, 12, 11, 13, 11, 11, 12, 13, 12, 14, 13, 16, 12, 12, 17, 13, 14, 13, 16, 13, 18, 14, 16, 15, 14, 17, 14, 15, 14, 14, 14, 17, 16, 19, 16, 17, 16, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For the corresponding term x1(n) see A254938(n).

See A254938 also for the Nagell reference.

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

LINKS

Table of n, a(n) for n=1..73.

FORMULA

A254938(n)^2 - 2*(2*a(n))^2 = -A007522(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

EXAMPLE

See A254938.

n = 3: 1^2 - 2*(2*2)^2 = 1 - 32  = -31 = -A007522(3).

CROSSREFS

Cf. A007522, A254938, A255233, A255234, A255246, A254935.

Sequence in context: A029122 A134482 A132921 * A181988 A194173 A028825

Adjacent sequences:  A255229 A255230 A255231 * A255233 A255234 A255235

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 18 2015

EXTENSIONS

More terms from Colin Barker, Feb 23 2015

STATUS

approved

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Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)