A254765 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).

1, 1, 3, 1, 5, 1, 3, 7, 3, 1, 7, 9, 1, 5, 7, 3, 5, 1, 9, 11, 7, 1, 9, 5, 11, 13, 11, 3, 7, 17, 11, 1, 7, 13, 3, 1, 7, 13, 5, 15, 21, 11, 7, 13, 5, 9, 1, 17, 23, 1

Offset

1,3

Comments

For the corresponding term x1(n) see A254764(n).

See A254764 for comments and 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 also prime 2) are given in A002335.

Links

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

Formula

A254764(n)^2 - 2*a(n)^2 = A007522(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

Example

A254764(4)^2 - 2*a(4)^2 = 7^2 - 2*1^2 = 47 = A007522(4).

Crossrefs

Cf. A007522, A254764, A254766, A254929, A254760, A254761, A254762, A254763, A002335.

Sequence in context: A154723 A273262 A274532 * A300893 A325249 A352453

Adjacent sequences: A254762 A254763 A254764 * A254766 A254767 A254768

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 12 2015

Status

approved