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).

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

Offset: 1

Author

Wolfdieter Lang, Feb 12 2015

Keywords

• nonn
• easy

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.

Examples

			See A254760.
n = 3: 9^2 - 2*(2*1)^2 = 81 - 8 = 73.
		

Crossrefs

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

Formula

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