A254935 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).

3, 5, 7, 7, 7, 9, 9, 11, 11, 11, 13, 15, 13, 13, 17, 15, 17, 19, 15, 17, 21, 17, 17, 21, 19, 23, 19, 19, 21, 23, 25, 21, 21, 27, 23, 29, 23, 23, 23, 23

Offset

1,1

Comments

For the corresponding term x1(n) see A254934(n).

See A254934 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 prime 2) are given in A255246.

Links

Table of n, a(n) for n=1..40.

Formula

A254934(n)^2 - 2*a(n)^2 = -A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

Example

See A254934.
n = 3: 5^2 - 2*7^2 = 25 - 98  = 73.

Crossrefs

Cf. A007519, A254934, A254936, A254937, A254938, A255232.

Sequence in context: A297346 A342622 A211517 * A104199 A103470 A316852

Adjacent sequences: A254932 A254933 A254934 * A254936 A254937 A254938

Keyword

nonn,look,easy

Author

Wolfdieter Lang, Feb 18 2015

Status

approved