A255234 - OEIS

A255234

One half of the fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A007522(n), n>=1 (primes congruent to 7 mod 8).

2, 3, 5, 4, 8, 5, 7, 11, 8, 7, 12, 14, 8, 11, 13, 10, 12, 10, 16, 18, 15, 11, 17, 14, 19, 21, 20, 14, 17, 26, 21, 14, 18, 23, 16, 15, 19, 24, 18, 26, 32, 23, 20, 25, 19, 22, 17, 29, 35, 18, 28, 25, 32, 21, 34, 19, 29, 23, 26, 31, 22, 33, 28, 37, 39, 41, 24

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A255233(n).

See the comments and the Nagell reference in A254938.

LINKS

Table of n, a(n) for n=1..67.

FORMULA

A255233(n)^2 - 2*(2*a(n))^2 = -A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.

a(n) = -(A254938(n) - 3*A255232(n)), n >= 1.

EXAMPLE

n = 2: 7^2 - 2*(2*3)^2 = 49 - 72 = -23 = - A007522(2).

a(3) = -(1 - 3*2) = 5.