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

1,1

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.

Links

Table of n, a(n) for n=1..50.

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.

Example

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.

Sequence in context: A349772 A088514 A357275 * A066677 A061026 A064632

Adjacent sequences: A254926 A254927 A254928 * A254930 A254931 A254932

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 11 2015

Status

approved