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A336786 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 10:27 EDT 2021. Contains 346359 sequences. (Running on oeis4.)