A341080 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5, where D is a prime number.

9, 11, 13, 453, 23461, 544557, 1537329309, 23841388917, 5420031851795067, 187413651300546981, 217796221885036092531, 177582465273740054778830373, 160849509983404119454318443146043, 608375445734704350836734541937669395740416570597

Offset: 1

Author

Christine Patterson, Feb 04 2021

Keywords

• nonn

Comments

Analogous to A033315 for x^2 - D*y^2 = 1, and D required to be prime.

Should 5 be inserted as the initial terms, and if so, should 5 (for D=5) be inserted at the beginning of A341079? - N. J. A. Sloane, Feb 20 2021

Examples

			For D=29, the least x for which x^2 - D*y^2 = 5 has a solution is 11. The next prime, D, for which x^2 - D*y^2 = 5 has a solution is 31, but the smallest x in this case is 6, which is less than 11. The next prime, D, after 31 for which x^2 - D*y^2 = 5 has a solution is 41 and the least x for which it has a solution is 13, which is larger than 11, so it is a new record value. 29 is a term of A341079 and 11 is a term of this sequence, but 31 is not a term of A341079 because the least x for which x^2 - D*y^2 = 5 has a solution is not a record value.
From _Jon E. Schoenfield_, Feb 18 2021: (Start)
As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = 5 begin as follows:
.
                x values           minimal
    D  satisfying x^2 - D*y^2 = 5  x value  record
   --  --------------------------  -------  ------
    2  (none)
    3  (none)
    5  5, 85, 1525, 27365, ...         5      *
    7  (none)
   11  4, 7, 73, 136, 1456, ...        4
   13  (none)
   17  (none)
   19  9, 48, 3012, 16311, ...         9      *
   29  11, 2251, 213371, ...          11      *
   31  6, 657, 17583, ...              6
   41  13, 397, 52877, ...            13      *
   59  8, 169, 8311, 179132, ...       8
   61  453, 9747957, ...             453      *
  ...
The record high values of x (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A341079. (End)
		

Links

• Christine Patterson, COCALC (Sage) Program

Crossrefs

Cf. A033315, A341079.