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Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -3, where D is a prime number.
2

%I #17 Feb 27 2021 21:50:32

%S 1,2,722,837158,77228318,5436980738,49637737974482,

%T 462761120757722506058,2836540596515452087502,

%U 37216095020093890760397134162,1858485134141860820807351059562927114738,42507485681147639763501995374671391449914

%N Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -3, where D is a prime number.

%H Christine Patterson, <a href="/A341078/a341078.txt">COCALC (Sage) Program</a>

%e From _Jon E. Schoenfield_, Feb 23 2021: (Start)

%e As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = -3 begin as follows:

%e .

%e x values satisfying minimal

%e D x^2 - D*y^2 = -5 y value record

%e -- ---------------------- ------- ------

%e 2 (none)

%e 3 1, 2, 7, 26, 97, ... 1 *

%e 5 (none)

%e 7 1, 2, 14, 31, 223, ... 1

%e 11 (none)

%e 13 2, 38, 2558, ... 2 *

%e 17 (none)

%e 19 1, 14, 326, 4759, ... 1

%e 23 (none)

%e 29 (none)

%e 31 2, 37, 604, ... 2

%e 37 (none)

%e 41 (none)

%e 43 2, 61, 13867, ... 2

%e 47 (none)

%e 53 (none)

%e 59 (none)

%e 61 722, 60158, ... 722 *

%e ...

%e The record high minimal values of y (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A341077. (End)

%Y Cf. A033315, A341077.

%K nonn

%O 1,2

%A _Christine Patterson_, Feb 04 2021

%E Edited by _Jon E. Schoenfield_, Feb 23 2021