A341084 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -5, where D is a prime number.

0, 16, 164, 1061372, 103068308, 162122886, 123398206659664, 2466743672871107188, 36438755210133838109283894464, 1957006192940494702014893262914, 541745559127518723115014358590896, 83890612389598737813497437560727166

Offset

1,2

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..12.

Christine Patterson, COCALC (Sage) Program

Example

For D=29, the least x for which x^2 - D*y^2 = -5 has a solution is 16. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest x in this case is 6, which is less than 16. The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least x for which it has a solution is 164, which is larger than 16, so it is a new record value. 29 is a term of A341083 and 16 is a term of this sequence, but 41 is not a term of A341083 because the least x for which x^2 - D*y^2 = -5 has a solution is not a record value.

Crossrefs

Cf. A033315, A341083.

Sequence in context: A274801 A274747 A204031 * A025930 A125404 A246057

Adjacent sequences: A341081 A341082 A341083 * A341085 A341086 A341087

Keyword

nonn

Author

Christine Patterson, Feb 13 2021

Extensions

a(1)=0 inserted by Jon E. Schoenfield, Feb 20 2021

Status

approved