A336788 Values of prime numbers, D, for incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = 2.

2, 31, 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, 53551, 58111, 62791

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

For D = 2, the least y for which x^2 - D*y^2 = 2 has a solution is 1.
The next primes, D, for which x^2 - D*y^2 = 2 has a solution are 7 and 23, but the smallest y in each of these cases is also 1, which is equal to the previous record y. So neither 7 nor 23 is a term.
The next prime, D, after 23 for which x^2 - D*y^2 = 2 has a solution is 31 and the least y for which it has a solution there is y = 7, which is larger than 1, so it is a new record y value. So 31 is a term here, and 7 is the corresponding term of A336789.

Crossrefs

Cf. A033316 (analogous for x^2 - D*y^2 = 1), A336786 (similar sequence for x's), A336789.

Sequence in context: A212569 A101254 A243472 * A107170 A273403 A291052

Adjacent sequences: A336785 A336786 A336787 * A336789 A336790 A336791

Keyword

nonn

Author

Christine Patterson, Aug 05 2020

Extensions

a(1) corrected and Example section edited by Jon E. Schoenfield, Feb 24 2021

Status

approved