A336795 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 3, where D is a prime number.

4, 8, 94, 9532, 289580, 3433342, 57427216, 1610590723242832, 422208570755689121370258391432928, 112180929726349239798469275333193570657564148, 8590101469813781580594707823194303692816416722

Offset

1,1

Comments

Analogous to A033315 for x^2 - D*y^2 = 1, and D required to be prime.

Links

Table of n, a(n) for n=1..11.

Christine Patterson, COCALC (Sage) program

Example

For D=73, the least x for which x^2 - D*y^2 = 3 has a solution is 94. The next prime, D, for which x^2 - D*y^2 = 3 has a solution is 97, but the smallest x in this case is 10, which is less than 94. The next prime, D, after 97 for which x^2 - D*y^2 = 3 has a solution is 109 and the least x for which it has a solution is 9532, which is larger than 94, so it is a new record value. 73 is a term of A336794 and 94 is a term of this sequence, but 97 is not a term of A336794 because the least x for which x^2 - 97*y^2 = 3 has a solution is not a record value.

Crossrefs

Cf. A033315, A336794.

Sequence in context: A331986 A057974 A071277 * A273060 A215844 A111100

Adjacent sequences: A336792 A336793 A336794 * A336796 A336797 A336798

Keyword

nonn

Author

Christine Patterson, Jan 17 2021

Extensions

Example section edited by Jon E. Schoenfield, Feb 23 2021

Status

approved