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

Author

Wolfdieter Lang, Feb 12 2015

Keywords

• nonn
• easy

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.

Examples

			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.

Formula

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