A254929 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).

3, 7, 5, 11, 7, 15, 13, 9, 17, 23, 13, 11, 27, 19, 17, 25, 23, 35, 19, 17, 25, 39, 23, 31, 21, 19, 25, 41, 33, 19, 29, 51, 37, 27, 49, 55, 41, 31, 47, 29, 23, 37, 45, 35, 51, 43, 63, 31, 25, 67

Offset: 1

Author

Wolfdieter Lang, Feb 11 2015

Keywords

• nonn
• easy

Comments

The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A254766(n).

See the comments and the Nagell reference in A254764.

Examples

			n = 2: 11^2 - 2*7^2 = 121 - 98 = 23.
The smallest positive solution is (x1(2), y1(2)) = (5, 1) from (A254764(2), A254765(2)).
See also A254766.
a(4) = 2*7 - 3*1 = 11.
		

Crossrefs

Cf. A007522, A254766, A254764,A254765, A254760, A254761, A254762, A254763.

Formula

A254766(n)^2 - 2*a(n)^2 = A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.

a(n) = 2*A254764(n) - 3*A254765(n), n >= 1.