A341081 Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2-D*y^2=5.

19, 61, 149, 241, 409, 421, 541, 1069, 1249, 1381, 1621, 4261, 4621, 4789, 6301, 8269, 12601, 12721, 14449, 16069, 20101, 32029, 33889, 34381, 35281, 38329, 43261, 45061, 60589, 87481, 89989, 97549, 99661, 121081, 125101, 166021, 178621, 187069, 191689, 202381

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Christine Patterson, COCALC (Sage) Program

Example

For D=19, the least positive y for which x^2-D*y^2=5 has a solution is 2. The next prime, D, for which x^2-D*y^2=5 has a solution is 29, but the smallest positive y in this case is 2, which is equal to the previous record y. So, 29 is not a term.
The next prime, D, after 19 for which x^2-D*y^2=5 has a solution is 61 and the least positive y for which it has a solution is y=58, which is larger than 2, so it is a new record y value. So 61 is in this sequence and 58 is in A341082.

Crossrefs

Cf. A033316 (analogous for x^2-D*y^2=1), A341079 (similar sequence for x's), A341082.

Sequence in context: A092327 A139498 A106087 * A201812 A262317 A214150

Adjacent sequences: A341078 A341079 A341080 * A341082 A341083 A341084

Keyword

nonn

Author

Christine Patterson, Feb 13 2021

Status

approved