

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).


5



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..69.


FORMULA

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


EXAMPLE

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.
Sequence in context: A077070 A075988 A029150 * A055923 A035634 A091563
Adjacent sequences: A255243 A255244 A255245 * A255247 A255248 A255249


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Feb 25 2015


EXTENSIONS

More terms from Colin Barker, Feb 26 2015


STATUS

approved



