A341080 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5, where D is a prime number.
9, 11, 13, 453, 23461, 544557, 1537329309, 23841388917, 5420031851795067, 187413651300546981, 217796221885036092531, 177582465273740054778830373, 160849509983404119454318443146043, 608375445734704350836734541937669395740416570597
Offset: 1
Keywords
Examples
For D=29, the least x for which x^2 - D*y^2 = 5 has a solution is 11. The next prime, D, for which x^2 - D*y^2 = 5 has a solution is 31, but the smallest x in this case is 6, which is less than 11. The next prime, D, after 31 for which x^2 - D*y^2 = 5 has a solution is 41 and the least x for which it has a solution is 13, which is larger than 11, so it is a new record value. 29 is a term of A341079 and 11 is a term of this sequence, but 31 is not a term of A341079 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 18 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 minimal
D satisfying x^2 - D*y^2 = 5 x value record
-- -------------------------- ------- ------
2 (none)
3 (none)
5 5, 85, 1525, 27365, ... 5 *
7 (none)
11 4, 7, 73, 136, 1456, ... 4
13 (none)
17 (none)
19 9, 48, 3012, 16311, ... 9 *
29 11, 2251, 213371, ... 11 *
31 6, 657, 17583, ... 6
41 13, 397, 52877, ... 13 *
59 8, 169, 8311, 179132, ... 8
61 453, 9747957, ... 453 *
...
The record high values of x (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A341079. (End)
Links
- Christine Patterson, COCALC (Sage) Program
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