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

1,1

Comments

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

Links

Table of n, a(n) for n=1..37.

Christine Patterson, COCALC (SageMath) program

Example

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.

Crossrefs

Cf. A033316, A336795.

Sequence in context: A316550 A244923 A146764 * A145474 A359666 A217606

Adjacent sequences: A336791 A336792 A336793 * A336795 A336796 A336797

Keyword

nonn

Author

Christine Patterson, Jan 17 2021

Status

approved