A336794 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 3.

13, 61, 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

Offset: 1

Author

Christine Patterson, Jan 17 2021

Keywords

• nonn

Comments

Analogous to A033316 for x^2-D*y^2=1, and D is required to be prime, and for record values of x.

Examples

			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 97. 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 97, so it is a new record value. 73 is a term of this sequence and 94 is a term of A336795, but 97 is not a term here because the least x for which x^2-D*y^2=3 has a solution at D=97 is not a record value.
		

Links

• Christine Patterson, COCALC (Sage) program

Crossrefs

Cf. A033316, A336795.