A336793 Incrementally largest values of minimal positive y satisfying the equation x^2 - D*y^2 = -2, where D is an odd prime number.

1, 3, 9, 27, 747, 36321, 2900979, 5843427, 563210019, 11516632737, 48957047673, 953426773899, 23440805582361, 27491112569139, 734940417828177, 1270701455204457, 106719437154440984241, 292398373544007804918339, 62392836359922644036329593, 607918712560763608313068257

Offset

1,2

Comments

For the corresponding numbers D see A336792.

Links

Table of n, a(n) for n=1..20.

Christine Patterson, Sage Program

Example

For D=3, the least positive y for which x^2-D*y^2=-2 has a solution is 1. The next prime, D, for which x^2-D*y^2=-2 has a solution is 11, but the smallest positive y in this case is also 1, which is equal to the previous record y. So 11 is not a term.
The next prime, D, after 11 for which x^2-D*y^2=-2 has a solution is 19 and the least positive y for which it has a solution is y=3, which is larger than 1, so it is a new record y value. So 19 is a term of A336792 and 3 is a term of this sequence.

Crossrefs

Cf. A033315, A336792.

Sequence in context: A018924 A061582 A175129 * A102558 A361986 A022767

Adjacent sequences: A336790 A336791 A336792 * A336794 A336795 A336796

Keyword

nonn

Author

Christine Patterson, Oct 14 2020

Status

approved