A341087 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 6.
3, 19, 43, 67, 139, 211, 571, 691, 883, 1483, 2011, 2539, 2851, 3331, 3931, 5779, 8011, 8779, 9811, 10459, 11131, 17851, 18379, 33331, 34819, 38299, 42571, 56659, 62731, 65179, 79699, 90931, 91939, 93811, 95419, 102859, 130579, 138139, 170179, 196771, 204019, 223939, 234259, 254731, 285139
Offset: 1
Keywords
Examples
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)
Links
- Christine Patterson, COCALC (Sage) Program
Extensions
a(1), a(2) inserted by Jon E. Schoenfield, Feb 20 2021
Comments