A341079 Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5.

5, 19, 29, 41, 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

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

Table of n, a(n) for n=1..42.

Christine Patterson, COCALC (Sage) Program

Example

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 this sequence and 11 is the corresponding term of A341080, but 31 is not a term of this sequence because at D=31 the least x for which x^2 - D*y^2 = 5 has a solution is not a record value.

Crossrefs

Cf. A033316, A341080.

Sequence in context: A161891 A296930 A251623 * A045456 A115167 A115103

Adjacent sequences: A341076 A341077 A341078 * A341080 A341081 A341082

Keyword

nonn

Author

Christine Patterson, Feb 04 2021

Extensions

a(1)=5 inserted and Example section edited by Jon E. Schoenfield, Feb 23 2021

Status

approved