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=139, the least x for which x^2 - D*y^2 = 6 has a solution is 59. The next prime, D, for which x^2 - D*y^2 = 6 has a solution is 163, but the smallest x in this case is 13, which is less than 59. The next prime, D, after 163 for which x^2 - D*y^2 = 6 has a solution is 211 and the least x for which it has a solution is 27265, which is larger than 59, so it is a new record value. So 139 is a term of this sequence and 59 is the corresponding term of A341088, but 163 is not a term here because the least x for which x^2 - D*y^2 = 6 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 = 6 begin as follows (with primes D for which there are no solutions omitted):
.
x values satisfying minimal
D x^2 - D*y^2 = 6 x value record
-- -------------------- ------- ------
3 3, 9, 33, 123, ... 3 *
19 5, 109, 1591, ... 5 *
43 7, 1541, 47207, ... 7 *
67 41, 3577, ... 41 *
139 59, 3945595, ... 59 *
163 13, 14921333, ... 13
211 27265, 30627659, ... 27265 *
...
The record high minimal values of x (marked with asterisks) are the terms of A341088. The corresponding values of D are the terms of this sequence. (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christine Patterson, Feb 13 2021
EXTENSIONS
a(1), a(2) inserted by Jon E. Schoenfield, Feb 20 2021
STATUS
approved