login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
COMMENTS
For the corresponding term x2(n) see A255247(n).
See the comments on A255247.
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).
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 19 2015
EXTENSIONS
More terms from Colin Barker, Feb 26 2015
STATUS
approved