A341076 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -3, where D is a prime number.
0, 2, 7, 11, 13, 5639, 11262809, 1538763335, 126460946201, 1276182285427369, 14786648025753749026871, 105410978030726984449289, 1498381179129960066289070257961, 107744062788861651804382809216696729188191, 2525173635632697805707745894621283442852191
Offset: 1
Keywords
Examples
For D=13, the least x for which x^2 - D*y^2 = -3 has a solution is 7. The next prime, D, for which x^2 - D*y^2 = -3 has a solution is 19, but the smallest x in this case is 4, which is less than 7. The next prime, D, after 19 for which x^2 - D*y^2 = -3 has a solution is 31 and the least x for which it has a solution is 11, which is larger than 7, so it is a new record value. x=11 is a term of this sequence and the corresponding value D=31 is a term of A336801, but 19 is not a term there because the least x for which x^2 - D*y^2 = -3 has a solution at D=19 is not a record value.
From _Jon E. Schoenfield_, Feb 23 2021: (Start)
As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = -3 begin as follows:
.
x values satisfying minimal
D x^2 - D*y^2 = -5 x value record
-- ---------------------- ------- ------
2 (none)
3 0, 3, 12, 45, 168, ... 0 *
5 (none)
7 2, 5, 37, 82, 590, ... 2 *
11 (none)
13 7, 137, 9223, ... 7 *
17 (none)
19 4, 61, 1421, ... 4
23 (none)
29 (none)
31 11, 206, 33646, ... 11 *
37 (none)
41 (none)
43 13, 400, 90932, ... 13 *
...
The record high minimal values of x (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A336801. (End)
Links
- Christine Patterson, COCALC (Sage) Program
Extensions
a(1)=0 inserted and Example section edited by Jon E. Schoenfield, Feb 23 2021
Comments