A341077 Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -3.

3, 13, 61, 181, 397, 541, 661, 1021, 1381, 1621, 3361, 3529, 4201, 4261, 4621, 6421, 9241, 9601, 9949, 12541, 20161, 23209, 25309, 32869, 37321, 43261, 71821, 78901, 82021, 112429, 127261, 131041, 137089, 139309, 144169, 169789, 183661, 226669, 300301

Offset

1,1

Links

Table of n, a(n) for n=1..39.

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 2. The next primes, D, for which x^2 - D*y^2 = -3 has a solution are 19, 31, and 43, but the smallest positive y in each of those cases is 1 or 2, neither of which is larger than the previous record y, 2. So 19, 31, and 43 are not terms of this sequence.
The next prime, D, after 43 for which x^2 - D*y^2 = -3 has a solution is 61, and the least positive y for which it has a solution is y=722, which is larger than 2, so it is a new record y value. So 61 is a term of this sequence and 722 is the corresponding term of A341078.

Crossrefs

Cf. A033316 (analogous for x^2 - D*y^2 = 1), A336801 (similar sequence for x's), A341078.

Sequence in context: A238445 A355298 A328704 * A357749 A112568 A104089

Adjacent sequences: A341074 A341075 A341076 * A341078 A341079 A341080

Keyword

nonn

Author

Christine Patterson, Feb 04 2021

Extensions

a(1) corrected and Example section edited by Jon E. Schoenfield, Feb 23 2021

Status

approved