A336786 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 2.

2, 7, 23, 31, 71, 103, 127, 151, 199, 271, 463, 631, 751, 919, 991, 1471, 1759, 1831, 1999, 2311, 2671, 3319, 4111, 4519, 4951, 5119, 6679, 8191, 8719, 10399, 11839, 12919, 13399, 15031, 16879, 19231, 21319, 23599, 26959, 30319, 32839, 34519, 37591, 38119, 43759, 48799

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..46.

Example

For D=31, the least x for which x^2-Dy^2=2 has a solution is 39. The next prime, D, for which x^2-Dy^2=2 has a solution is 47, but the smallest x in this case is 7, which is less than 39. The next prime, D, after 47 for which x^2-Dy^2=2 has a solution is 71 and the least x for which it has a solution is x=59, which is larger than 39, so it is a new record value. 71 is a term of this sequence and 59 is a term of A336787. 47 is not a term here because the least x for which x^2-47y^2=2 has a solution is not a record value.

Crossrefs

Cf. A033316.

Sequence in context: A045382 A049560 A049588 * A106020 A248602 A045383

Adjacent sequences: A336783 A336784 A336785 * A336787 A336788 A336789

Keyword

nonn

Author

Christine Patterson, Aug 05 2020

Status

approved