

A255248


Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2  2*y^2 = A001132(n), n>=1 (primes congruent to {1,7} mod 8)


4



4, 7, 6, 10, 9, 8, 16, 11, 10, 15, 19, 14, 13, 22, 17, 16, 14, 24, 19, 28, 16, 27, 22, 31, 21, 26, 20, 19, 24, 29, 37, 21, 20, 32, 36, 31, 25, 30, 23, 22, 43, 29, 34, 28, 38, 42, 25, 45, 49, 29, 40, 35, 28, 27, 34, 39, 52, 43, 42, 28, 36, 46, 41, 35, 33, 32
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

For the corresponding term x2(n) see A255247(n).
See the comments on A255247.


LINKS

Table of n, a(n) for n=1..66.


FORMULA

A255247(n)^2  2*a(n)^2 = A001132(n), n >= 1, gives the second smallest positive (proper) solution of this (generalized) Pell equation.
a(n) = (2*A255235(n+1)  3*A255246(n+1)), n >= 1.


EXAMPLE

See A255247.
a(4) = (2*1  3*4) = 12  2 = 10.
n=4: 13^2  2*10^2 = 169  200 = 31 = A001132(4).


CROSSREFS

Cf. A001132, A255247, A255235, A255246, A254937, A255234, A254931.
Sequence in context: A293904 A069286 A079354 * A122460 A256659 A063845
Adjacent sequences: A255245 A255246 A255247 * A255249 A255250 A255251


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Feb 19 2015


EXTENSIONS

More terms from Colin Barker, Feb 26 2015


STATUS

approved



