A341083 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -5.
5, 29, 61, 109, 181, 641, 661, 1021, 1549, 2161, 2389, 3169, 3469, 4909, 5581, 8929, 9601, 9949, 12841, 13381, 14029, 17029, 21169, 24709, 25309, 28729, 31249, 32869, 34549, 35149, 39901, 40429, 43801, 48049, 49009, 56401, 56701, 62701, 63541, 70141, 86269, 91009
Offset: 1
Keywords
Examples
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.
From _Jon E. Schoenfield_, Feb 20 2021: (Start)
As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = -5 begin as follows:
.
x values satisfying minimal
D x^2 - D*y^2 = -5 x value record
-- --------------------- ------- ------
2 (none)
3 (none)
5 0, 20, 360, 6460, ... 0 *
7 (none)
11 (none)
13 (none)
17 (none)
19 (none)
23 (none)
29 16, 1524, 315156, ... 16 *
31 (none)
37 (none)
41 6, 826, 25414, ... 6
43 (none)
47 (none)
51 (none)
53 (none)
59 (none)
61 164, 26924344, ... 164 *
...
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)
Links
- Christine Patterson, COCALC (Sage) Program
Extensions
a(1)=5 inserted and Example section edited by Jon E. Schoenfield, Feb 20 2021
Comments