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

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.
See also A255233.

Crossrefs

Cf. A007522, A255233, A254938, A255232, A254937.

Sequence in context: A249328 A083464 A347423 * A364225 A256995 A249129

Adjacent sequences: A255231 A255232 A255233 * A255235 A255236 A255237

Keyword

nonn,look,easy

Author

Wolfdieter Lang, Feb 19 2015

Extensions

More terms from Colin Barker, Feb 24 2015

Status

approved