login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264439 The y member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for even D(n) = A264354(n). 2
1, 17, 1, 49, 21287, 1, 23, 97, 1, 48727, 161, 151, 1, 21387679, 241, 1826021057, 1, 11692649642023, 7, 337, 3903396217, 1, 294125365483681, 17, 449, 7, 1994828801, 1, 6399911, 4798348971487087, 577, 119, 7867888313, 1, 437071, 161131189369, 721, 273849896195263, 20783, 262759 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding x2(n) value is given by A264438(n). The positive fundamental solution (x1(n), y1(n)) of the first class is given by (2*A261247(n), A261248(n)).

There is only one class of proper solutions for those D = D(n) = A264354(n) values leading to (x1(n), y1(n)) = (x2(n), y2(n)).

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

n=1: D(1) = 8, (2*2)^2 - 8*1^2 = +8. The first class positive fundamental solution was identical, thus there is only one class of proper solutions for D = 8.

n=5: D(5) = 124, (2*118521)^2 - 124*21287^2 = +8. The first class solution was (2*39)^2 - 124*7^2 = +8. Thus there are two classes, conjugated to each other for this D value.

CROSSREFS

Cf. A264354, A261247 (x1/2), A261248 (y1), A264438 (x2/2), A263012 (odd D), A264349, A264350, A264351, A264353.

Sequence in context: A040305 A189120 A102292 * A279363 A295576 A223519

Adjacent sequences:  A264436 A264437 A264438 * A264440 A264441 A264442

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Nov 19 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 22 20:37 EDT 2019. Contains 326186 sequences. (Running on oeis4.)