A336796 Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = 3.

13, 73, 109, 157, 241, 277, 421, 1549, 3061, 4561, 4861, 5701, 6301, 6829, 8941, 10429, 13381, 14029, 14221, 21169, 22369, 24049, 26161, 29761, 30529, 33601, 39901, 44221, 45061, 47581, 55609, 61609, 62869, 64381, 74869, 97549, 121501, 129061, 133669, 135661

Offset

1,1

Comments

Is 61 the only term where this differs from A336794? - R. J. Mathar, Feb 16 2021

Links

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

Christine Patterson, COCALC (Sage) program

Example

For D=13, the least positive y for which x^2-D*y^2=3 has a solution is 1. The next prime, D, for which x^2-D*y^2=3 has a solution is 61, but the smallest positive y in this case is also 1, which is equal to the previous record y. So, 61 is not a term.
The next prime, D, after 61 for which x^2-D*y^2=3 has a solution is 73, and the least positive y for which it has a solution in this case is y=11, which is larger than 1, so it is a new record y value. So, 73 is a term in this sequence and 11 is a term in A336800.

Crossrefs

Cf. A033316 (analog for x^2-D*y^2=1), A336790 (similar sequence for x's), A336800, A336794.

Sequence in context: A139849 A139911 A097460 * A138353 A097402 A255416

Adjacent sequences: A336793 A336794 A336795 * A336797 A336798 A336799

Keyword

nonn

Author

Christine Patterson, Jan 17 2021

Status

approved