A254763 One half of the fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = A007519(n), n>=1 (primes congruent to 1 mod 8).

2, 4, 6, 5, 4, 8, 7, 9, 7, 6, 11, 14, 9, 7, 16, 11, 15, 18, 8, 14, 20, 10, 9, 19, 15, 22, 14, 13, 16, 20, 23, 13, 11, 25, 17, 28, 16, 15, 14, 13, 23, 18, 26, 29, 16, 32, 13, 20, 28, 24

Offset

1,1

Comments

The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A254762(n).

See the comments and the Nagell reference in A254760.

Links

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

Formula

A254762(n)^2 - 2*(2*a(n))^2 = A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.

a(n) = A254760(n) - 3*A254761(n), n >= 1.

Example

n = 2: 13^2 - 2*(2*4)^2 = 169 - 128 = 41.
The smallest positive solution is (x1(2), y1(2)) = (7, 2) from (A254760(2), 2*A254761(2)).
See also A254762.
a(4) = 11 - 3*2 = 5.

Crossrefs

Cf. A007519, A005123, A254762, A254760, 2*A254761.

Sequence in context: A071288 A063892 A353650 * A023825 A022485 A230631

Adjacent sequences: A254760 A254761 A254762 * A254764 A254765 A254766

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 10 2015

Status

approved