A255246 Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A038873(n), n>=1 (primes congruent to {1,2,7} mod 8).

3, 2, 3, 4, 4, 5, 6, 6, 7, 8, 7, 7, 8, 9, 8, 9, 10, 12, 10, 11, 10, 14, 11, 12, 11, 13, 12, 14, 15, 14, 13, 13, 17, 18, 14, 14, 15, 17, 16, 19, 20, 15, 17, 16, 18, 16, 16, 21, 17, 17, 21, 18, 19, 22, 23, 20, 19, 18, 19, 20, 26, 22, 20, 21, 23, 25, 26, 28, 21

Offset

1,1

Comments

For the corresponding term x1(n) see A255235(n).

For the primes 1 (mod 8) see A154935, and for the primes 7 (mod 8) see 2*A255232.

See A254934 and A254938 also for the derivation based on the Nagell reference given there.

Links

Table of n, a(n) for n=1..69.

Formula

A255235(n)^2 - 2*a(n)^2 = -A038873(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

Example

See A255235.
n = 1: 4^2 - 2*3^2 = -2 = -A038873(1),
n = 3: 1^2 - 2*3^2 = 1 - 18 = -17 = -A038873(3).

Crossrefs

Cf. A038873, A255235, A255247, A255248, A254935, 2*A255232, A002335.

Sequence in context: A077070 A075988 A029150 * A055923 A035634 A091563

Adjacent sequences: A255243 A255244 A255245 * A255247 A255248 A255249

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 25 2015

Extensions

More terms from Colin Barker, Feb 26 2015

Status

approved