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A336789 Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = 2, where D is a prime number. 1
1, 7, 47, 193, 3383, 9041, 20687, 731153, 8808724183, 98546821297, 2208304390649, 19569442212887, 162848901149273, 311991807873328639, 1023490545293318137, 1419456983764900351, 13170848364266136042527, 1276022762028643136592313, 14225223924067129319855681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

For D=2, the least y for which x^2 - D*y^2 = 2 has a solution is 1. The next primes, D, for which x^2 - D*y^2 = 2 has a solution are 7 and 23, but the smallest y in each of these cases is also 1, which is equal to the previous record y. So 7 and 23 are not terms of A336788.

The next prime, D, after 23 for which x^2 - D*y^2 = 2 has a solution is 31 and the least y for which it has a solution there is y=7, which is larger than 1, so it is a new record y value. So 31 is a term of A336788, and 7 is the corresponding term here.

From Jon E. Schoenfield, Feb 24 2021: (Start)

Primes D for which the equation x^2 - D*y^2 = 2 has integer solutions begin 2, 7, 23, 31, 47, 71, 79, 103, ...; at those values of D, the minimal y values satisfying the equation x^2 - D*y^2 = 2 begin as follows:

.

         x values satisfying     minimal

    D      x^2 - D*y^2 = 2       y value  record

  ---  ------------------------  -------  ------

    2  1, 7, 41, 239, 1393, ...      1       *

    7  1, 17, 271, 4319, ...         1

   23  1, 49, 2351, 112799, ...      1

   31  7, 21287, 64712473, ...       7       *

   47  1, 97, 9311, 893759, ...      1

   71  7, 48727, 339139913, ...      7

   79  1, 161, 25759, ...            1

  103  47, 21387679, ...            47       *

  ...

The record high minimal values of y (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A336788. (End)

CROSSREFS

Cf. A033315, A336788.

Sequence in context: A046872 A167860 A152988 * A201437 A202509 A009202

Adjacent sequences:  A336786 A336787 A336788 * A336790 A336791 A336792

KEYWORD

nonn

AUTHOR

Christine Patterson, Oct 14 2020

EXTENSIONS

Example section edited by Jon E. Schoenfield, Feb 24 2021

STATUS

approved

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)