A254761 One half of the fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = A007519(n), n >= 1 (primes congruent to 1 mod 8).

1, 1, 1, 2, 3, 1, 2, 2, 4, 5, 2, 1, 4, 6, 1, 4, 2, 1, 7, 3, 1, 7, 8, 2, 4, 1, 5, 6, 5, 3, 2, 8, 10, 2, 6, 1, 7, 8, 9, 10, 4, 7, 3, 2, 9, 1, 12, 7, 3, 5

Offset

1,4

Comments

For the corresponding term x1(n) see A254760(n).

See A254760 also for the Nagell reference.

The least positive y solutions (that is the ones of the first class) for the primes +1 and -1 (mod 8) together (including in the first class also prime 2) are given in A002335.

Links

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

Formula

A254760(n)^2 - 2*(2*a(n))^2 = A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

Example

See A254760.
n = 3: 9^2 - 2*(2*1)^2 = 81 - 8 = 73.

Crossrefs

Cf. A007519, A254760, A254762, 2*A254763, A002335.

Sequence in context: A227781 A366294 A351441 * A227552 A205003 A159956

Adjacent sequences: A254758 A254759 A254760 * A254762 A254763 A254764

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 12 2015

Status

approved