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%I #12 Feb 20 2021 23:09:27
%S 5,29,61,109,181,641,661,1021,1549,2161,2389,3169,3469,4909,5581,8929,
%T 9601,9949,12841,13381,14029,17029,21169,24709,25309,28729,31249,
%U 32869,34549,35149,39901,40429,43801,48049,49009,56401,56701,62701,63541,70141,86269,91009
%N Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -5.
%C Analogous to A033316 for x^2 - D*y^2 = 1, and D is required to be prime, and for record values of x.
%H Christine Patterson, <a href="/A341083/a341083.txt">COCALC (Sage) Program</a>
%e For D=29, the least x for which x^2 - D*y^2 = -5 has a solution is 16. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest x in this case is 6, which is less than 16. The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least x for which it has a solution is 164, which is larger than 16, so it is a new record value. So 29 is a term of this sequence and 16 is the corresponding term of A341084, but 41 is not a term here because the least x for which x^2 - D*y^2 = -5 has a solution is not a record value.
%e From _Jon E. Schoenfield_, Feb 20 2021: (Start)
%e As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = -5 begin as follows:
%e .
%e x values satisfying minimal
%e D x^2 - D*y^2 = -5 x value record
%e -- --------------------- ------- ------
%e 2 (none)
%e 3 (none)
%e 5 0, 20, 360, 6460, ... 0 *
%e 7 (none)
%e 11 (none)
%e 13 (none)
%e 17 (none)
%e 19 (none)
%e 23 (none)
%e 29 16, 1524, 315156, ... 16 *
%e 31 (none)
%e 37 (none)
%e 41 6, 826, 25414, ... 6
%e 43 (none)
%e 47 (none)
%e 51 (none)
%e 53 (none)
%e 59 (none)
%e 61 164, 26924344, ... 164 *
%e ...
%e The record high minimal values of x (marked with asterisks) are the terms of A341084. The corresponding values of D are the terms of this sequence. (End)
%Y Cf. A033316, A341084.
%K nonn
%O 1,1
%A _Christine Patterson_, Feb 13 2021
%E a(1)=5 inserted and Example section edited by _Jon E. Schoenfield_, Feb 20 2021