OFFSET
1,1
COMMENTS
Analogous to A033316 for x^2 - D*y^2 = 1, and D is required to be prime, and for record values of x.
LINKS
Christine Patterson, COCALC (Sage) Program
EXAMPLE
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)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christine Patterson, Feb 13 2021
EXTENSIONS
a(1)=5 inserted and Example section edited by Jon E. Schoenfield, Feb 20 2021
STATUS
approved