A336794 -id:A336794 - cp's OEIS frontend

A336795 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 3, where D is a prime number.

4, 8, 94, 9532, 289580, 3433342, 57427216, 1610590723242832, 422208570755689121370258391432928, 112180929726349239798469275333193570657564148, 8590101469813781580594707823194303692816416722

Offset: 1

Christine Patterson, Jan 17 2021

nonn

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

			For D=73, the least x for which x^2 - D*y^2 = 3 has a solution is 94. The next prime, D, for which x^2 - D*y^2 = 3 has a solution is 97, but the smallest x in this case is 10, which is less than 94. The next prime, D, after 97 for which x^2 - D*y^2 = 3 has a solution is 109 and the least x for which it has a solution is 9532, which is larger than 94, so it is a new record value. 73 is a term of A336794 and 94 is a term of this sequence, but 97 is not a term of A336794 because the least x for which x^2 - 97*y^2 = 3 has a solution is not a record value.

Christine Patterson, COCALC (Sage) program

Cf. A033315, A336794.

Example section edited by Jon E. Schoenfield, Feb 23 2021

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

Original entry on oeis.org

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

Christine Patterson, Jan 17 2021

nonn

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

			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.

Christine Patterson, COCALC (Sage) program

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

cp's OEIS Frontend

A336795 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 3, where D is a prime number.

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