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

Author

Wolfdieter Lang, Feb 25 2015

Keywords

• nonn
• easy

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.

Examples

			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.

Formula

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

Extensions

More terms from Colin Barker, Feb 26 2015