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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A255235 Fundamental positive solution x = x1(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
4, 1, 1, 3, 1, 3, 5, 1, 5, 7, 3, 1, 5, 7, 1, 5, 7, 11, 3, 7, 1, 13, 3, 7, 1, 9, 5, 11, 13, 9, 5, 1, 15, 17, 5, 3, 7, 13, 9, 17, 19, 1, 11, 7, 13, 5, 3, 19, 3, 1, 17, 7, 11, 19, 21, 13, 9, 1, 7, 9, 25, 15, 7, 11, 17, 21, 23, 27, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the corresponding term y1(n) see A255246(n).

The present solutions of this first class are the smallest positive ones.

For the positive fundamental proper (sometimes called primitive) solutions x2 and y2 of the second class of this (generalized) Pell equation see A255247 and A255248. There is no second class for prime 2.

For the first class solutions of this Pell equation with primes 1 (mod 8) see A254934 and A254935. For those with primes 7 (mod 8) see A254938 and 2*A255232. For the derivation of these solutions see A254934 and A254938, also for the Nagell reference.

LINKS

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

FORMULA

a(n)^2 - A255246(n)^2 = - A038873(n), n >= 1,  gives the smallest positive (proper) solution of this (generalized) Pell equation.

EXAMPLE

The first pairs [x1(n), y1(n)] of the fundamental positive solutions of this first class are

  (the prime A038873(n) is listed as first entry):

  [2,[4, 3]], [7, [1, 2]], [17, [1, 3]],

  [23, [3, 4]], [31, [1, 4]], [41, [3, 5]],

  [47, [5, 6]], [71, [1, 6]], [73, [5, 7]],

  [79, [7, 8]], [89, [3, 7]], [97, [1, 7]],

  [103, [5, 8]], [113, [7, 9]], [127, [1, 8]],

  [137, [5, 9]], [151, [7, 10]], [167, [11, 12]], [191, [3, 10]], [193, [7, 11]], [199, [1, 10]], [223, [13, 14]], [233, [3, 11]], [239, [7, 12]], [241, [1, 11]], [257, [9, 13]], [263, [5, 12]], ...

n=1: 4^2 - 2*3^2 = -2 = -A038873(1),

n=2: 1^2 - 2*2^2 = 1 - 8 = -7 = -A038873(2).

CROSSREFS

Cf. A038873, A255246, A255247, A255248, A254934, A254935, A254938, 2*A255232, A002334.

Sequence in context: A111311 A327893 A326410 * A293882 A016524 A087963

Adjacent sequences:  A255232 A255233 A255234 * A255236 A255237 A255238

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 25 2015

EXTENSIONS

More terms from Colin Barker, Feb 26 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 December 14 14:20 EST 2019. Contains 329979 sequences. (Running on oeis4.)