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EXAMPLE
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For D=13, the least x for which x^2 - D*y^2 = -3 has a solution is 7. The next prime, D, for which x^2 - D*y^2 = -3 has a solution is 19, but the smallest x in this case is 4, which is less than 7. The next prime, D, after 19 for which x^2 - D*y^2 = -3 has a solution is 31 and the least x for which it has a solution is 11, which is larger than 7, so it is a new record value. x=11 is a term of this sequence and the corresponding value D=31 is a term of A336801, but 19 is not a term there because the least x for which x^2 - D*y^2 = -3 has a solution at D=19 is not a record value.
As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = -3 begin as follows:
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x values satisfying minimal
D x^2 - D*y^2 = -5 x value record
-- ---------------------- ------- ------
2 (none)
3 0, 3, 12, 45, 168, ... 0 *
5 (none)
7 2, 5, 37, 82, 590, ... 2 *
11 (none)
13 7, 137, 9223, ... 7 *
17 (none)
19 4, 61, 1421, ... 4
23 (none)
29 (none)
31 11, 206, 33646, ... 11 *
37 (none)
41 (none)
43 13, 400, 90932, ... 13 *
...
The record high minimal values of x (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A336801.
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