A341078 Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -3, where D is a prime number.

1, 2, 722, 837158, 77228318, 5436980738, 49637737974482, 462761120757722506058, 2836540596515452087502, 37216095020093890760397134162, 1858485134141860820807351059562927114738, 42507485681147639763501995374671391449914

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Christine Patterson, COCALC (Sage) Program

Example

From Jon E. Schoenfield, Feb 23 2021: (Start)
As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = -3 begin as follows:
.
       x values satisfying    minimal
   D     x^2 - D*y^2 = -5     y value  record
  --  ----------------------  -------  ------
   2  (none)
   3  1, 2, 7, 26, 97, ...        1      *
   5  (none)
   7  1, 2, 14, 31, 223, ...      1
  11  (none)
  13  2, 38, 2558, ...            2      *
  17  (none)
  19  1, 14, 326, 4759, ...       1
  23  (none)
  29  (none)
  31  2, 37, 604, ...             2
  37  (none)
  41  (none)
  43  2, 61, 13867, ...           2
  47  (none)
  53  (none)
  59  (none)
  61  722, 60158, ...           722      *
...
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 A341077. (End)

Crossrefs

Cf. A033315, A341077.

Sequence in context: A028367 A000197 A036298 * A153923 A167440 A156008

Adjacent sequences: A341075 A341076 A341077 * A341079 A341080 A341081

Keyword

nonn

Author

Christine Patterson, Feb 04 2021

Extensions

Edited by Jon E. Schoenfield, Feb 23 2021

Status

approved