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%I #24 Feb 20 2021 01:01:09
%S 9,11,13,453,23461,544557,1537329309,23841388917,5420031851795067,
%T 187413651300546981,217796221885036092531,177582465273740054778830373,
%U 160849509983404119454318443146043,608375445734704350836734541937669395740416570597
%N Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5, where D is a prime number.
%C Analogous to A033315 for x^2 - D*y^2 = 1, and D required to be prime.
%C Should 5 be inserted as the initial terms, and if so, should 5 (for D=5) be inserted at the beginning of A341079? - _N. J. A. Sloane_, Feb 20 2021
%H Christine Patterson, <a href="/A341080/a341080.txt">COCALC (Sage) Program</a>
%e For D=29, the least x for which x^2 - D*y^2 = 5 has a solution is 11. The next prime, D, for which x^2 - D*y^2 = 5 has a solution is 31, but the smallest x in this case is 6, which is less than 11. The next prime, D, after 31 for which x^2 - D*y^2 = 5 has a solution is 41 and the least x for which it has a solution is 13, which is larger than 11, so it is a new record value. 29 is a term of A341079 and 11 is a term of this sequence, but 31 is not a term of A341079 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 18 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 minimal
%e D satisfying x^2 - D*y^2 = 5 x value record
%e -- -------------------------- ------- ------
%e 2 (none)
%e 3 (none)
%e 5 5, 85, 1525, 27365, ... 5 *
%e 7 (none)
%e 11 4, 7, 73, 136, 1456, ... 4
%e 13 (none)
%e 17 (none)
%e 19 9, 48, 3012, 16311, ... 9 *
%e 29 11, 2251, 213371, ... 11 *
%e 31 6, 657, 17583, ... 6
%e 41 13, 397, 52877, ... 13 *
%e 59 8, 169, 8311, 179132, ... 8
%e 61 453, 9747957, ... 453 *
%e ...
%e The record high values of x (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A341079. (End)
%Y Cf. A033315, A341079.
%K nonn
%O 1,1
%A _Christine Patterson_, Feb 04 2021
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