A336801 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -3.

3, 7, 13, 31, 43, 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

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..36.

Christine Patterson, COCALC (Sage) Program

Example

For D=13, the least x for which x^2 - D*y^2 = -3 has a solution is 7. The next prime, D, for which x^2 - D*y^2 = -3 has a solution is 19, but the smallest x in this case is 4, which is less than 7. The next prime, D, after 19 for which x^2 - D*y^2 = -3 has a solution is 31 and the least x for which it has a solution is 11, which is larger than 7, so it is a new record value. D=13 is a term of this sequence and x=7 is a term of A341076, but D=19 is not a term here because at D=19 the least x for which x^2 - D*y^2 = -3 has a solution is not a record value.

Crossrefs

Cf. A033316, A341076.

Sequence in context: A243765 A256148 A083520 * A162869 A079018 A342150

Adjacent sequences: A336798 A336799 A336800 * A336802 A336803 A336804

Keyword

nonn

Author

Christine Patterson, Feb 04 2021

Extensions

a(1)=3 inserted and Example section edited by Jon E. Schoenfield, Feb 23 2021

Status

approved