A336790 Values of odd prime numbers, D, for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -2.

3, 11, 19, 43, 67, 139, 211, 331, 379, 571, 739, 859, 1051, 1291, 1531, 1579, 1699, 2011, 2731, 3019, 3259, 3691, 3931, 5419, 5659, 5779, 6211, 6379, 6451, 8779, 9619, 10651, 16699, 17851, 18379, 21739, 25939, 32971, 42331, 42571, 44851, 50131, 53299, 55819, 56611, 60811, 61051, 73459, 76651, 90619, 90931

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..51.

Example

For D=43, the least x for which x^2-D*y^2=-2 has a solution is 59. The next prime, D, for which x^2-D*y^2=-2 has a solution is 59, but the smallest x in this case is 23, which is less than 59. The next prime, D, after 59 for which x^2-D*y^2=-2 has a solution is 67 and the least x for which it has a solution is 221, which is larger than 59, so it is a new record value. 67 is a term of this sequence and 221 is a term of A336791, but 59 is not a term here because the least x for which x^2-47*y^2=-2 has a solution at D=59 is not a record value.

Crossrefs

Cf. A033315, A336791.

Sequence in context: A294912 A309027 A213891 * A163851 A213051 A238362

Adjacent sequences: A336787 A336788 A336789 * A336791 A336792 A336793

Keyword

nonn

Author

Christine Patterson, Oct 14 2020

Status

approved