proposed

reviewed

editing

proposed

Incrementally largest values of minimal y satisfying the equation x^2-D*y^2=6, where D is a prime number.

1, 5, 1877, 194255, 1730497, 45323015, 201492029, 397602538755575, 497108717282761, 7938459500809177705, 4015742266482169869985, 594448160241453500681390645, 1484161662562368548711372281538395, 2767866378797656254852541954053955, 504110847457236772029549084857628475205

1,2

Christine Patterson, <a href="/A341090/a341090.txt">COCALC (Sage) Program</a>

For D=67, the least positive y for which x^2-D*y^2=6 has a solution is 5. The next prime, D, for which x^2-D*y^2=6 has a solution is 139, but the smallest positive y in this case is 5, which is equal to the previous record y. So, 139 is not a term.

The next prime, D, after 67 for which x^2-D*y^2=6 has a solution is 211 and the least positive y for which it has a solution is y=1877, which is larger than 5, so it is a new record y value. So, 67 qualifies for membership to sequence A341089 and 1877 qualifies for membership to this sequence.

As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = 6 begin as follows:

y values satisfying minimal

D x^2 - D*y^2 = 6 y value record

-- --------------------- ------- ------

2 (none)

3 (none)

5 (none)

7 (none)

11 (none)

13 (none)

17 (none)

19 (none)

23 (none)

29 (none)

31 (none)

37 (none)

41 (none)

43 1, 235, 7199... 7 *

47 (none)

53 (none)

59 (none)

61 (none)

67 41, 3577, ... 41 *

The record high minimal values of y (marked with asterisks) are the terms of A341087. The corresponding values of D are the terms of this sequence. (End)

Cf. A033315, A341089.

nonn

recycled

Christine Patterson, Feb 23 2021

As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = 6 begin as follows:

y values satisfying minimal

D x^2 - D*y^2 = 6 y value record

-- --------------------- ------- ------

2 (none)

3 (none)

5 (none)

7 (none)

11 (none)

13 (none)

17 (none)

19 (none)

23 (none)

29 (none)

31 (none)

37 (none)

41 (none)

43 1, 235, 7199... 7 *

47 (none)

53 (none)

59 (none)

61 (none)

67 41, 3577, ... 41 *

The record high minimal values of y (marked with asterisks) are the terms of A341087. The corresponding values of D are the terms of this sequence. (End)

allocated for Christine PattersonIncrementally largest values of minimal y satisfying the equation x^2-D*y^2=6, where D is a prime number.

1, 5, 1877, 194255, 1730497, 45323015, 201492029, 397602538755575, 497108717282761, 7938459500809177705, 4015742266482169869985, 594448160241453500681390645, 1484161662562368548711372281538395, 2767866378797656254852541954053955, 504110847457236772029549084857628475205

1,2

Christine Patterson, <a href="/A341090/a341090.txt">COCALC (Sage) Program</a>

For D=67, the least positive y for which x^2-D*y^2=6 has a solution is 5. The next prime, D, for which x^2-D*y^2=6 has a solution is 139, but the smallest positive y in this case is 5, which is equal to the previous record y. So, 139 is not a term.

The next prime, D, after 67 for which x^2-D*y^2=6 has a solution is 211 and the least positive y for which it has a solution is y=1877, which is larger than 5, so it is a new record y value. So, 67 qualifies for membership to sequence A341089 and 1877 qualifies for membership to this sequence.

Cf. A033315, A341089.

allocated

nonn

Christine Patterson, Feb 23 2021

approved

editing

allocated for Christine Patterson

allocated

approved