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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
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, 6, 1, 7, 8, 9, 10, 4, 7, 3, 2, 9, 1, 12, 7, 3, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For the corresponding term x1(n) see A254760(n).

See A254760 also for the Nagell reference.

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.

LINKS

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

FORMULA

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

EXAMPLE

See A254760.

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

CROSSREFS

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

Sequence in context: A236855 A244232 A227781 * A227552 A205003 A159956

Adjacent sequences:  A254758 A254759 A254760 * A254762 A254763 A254764

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 12 2015

STATUS

approved

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)