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A341080 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5, where D is a prime number.

%I A341080 #24 Feb 20 2021 01:01:09
%S A341080 9,11,13,453,23461,544557,1537329309,23841388917,5420031851795067,
%T A341080 187413651300546981,217796221885036092531,177582465273740054778830373,
%U A341080 160849509983404119454318443146043,608375445734704350836734541937669395740416570597
%N A341080 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5, where D is a prime number.
%C A341080 Analogous to A033315 for x^2 - D*y^2 = 1, and D required to be prime.
%C A341080 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 A341080 Christine Patterson, <a href="/A341080/a341080.txt">COCALC (Sage) Program</a>
%e A341080 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 A341080 From _Jon E. Schoenfield_, Feb 18 2021: (Start)
%e A341080 As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = 5 begin as follows:
%e A341080 .
%e A341080                 x values           minimal
%e A341080     D  satisfying x^2 - D*y^2 = 5  x value  record
%e A341080    --  --------------------------  -------  ------
%e A341080     2  (none)
%e A341080     3  (none)
%e A341080     5  5, 85, 1525, 27365, ...         5      *
%e A341080     7  (none)
%e A341080    11  4, 7, 73, 136, 1456, ...        4
%e A341080    13  (none)
%e A341080    17  (none)
%e A341080    19  9, 48, 3012, 16311, ...         9      *
%e A341080    29  11, 2251, 213371, ...          11      *
%e A341080    31  6, 657, 17583, ...              6
%e A341080    41  13, 397, 52877, ...            13      *
%e A341080    59  8, 169, 8311, 179132, ...       8
%e A341080    61  453, 9747957, ...             453      *
%e A341080   ...
%e A341080 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 A341080 Cf. A033315, A341079.
%K A341080 nonn
%O A341080 1,1
%A A341080 _Christine Patterson_, Feb 04 2021