A374160 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 11*y^2 = k.

0, 12, 60, 180, 540, 1620, 2700, 8100, 12420, 20700, 37260, 1180980, 62100, 476100, 335340, 186300, 310500, 1822500, 558900, 53144100, 931500, 1676700, 4284900, 324860625, 1925100, 4657500, 244462860, 12854700, 8383500

Offset

0,2

Comments

a(n) is the smallest nonnegative k such that A374017(k) = n.

a(30) = 5775300.

a(31) = 38564100.

a(32) = 9625500.

a(33) = 135812700.

a(35) = 41917500.

a(36) = 17325900.

a(37) = 107122500.

a(40) = 28876500.

Links

Table of n, a(n) for n=0..28.

Prog

(Python)
from itertools import count
from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A374160(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x**2+11*y**2-m) if d[0]>0 and d[1]>0)==n) # Chai Wah Wu, Jun 30 2024

Crossrefs

Cf. A328151, A343105, A374158, A374159, A374161.

Cf. A374017.

Sequence in context: A033486 A112415 A174642 * A061624 A213818 A004302

Adjacent sequences: A374157 A374158 A374159 * A374161 A374162 A374164

Keyword

nonn,more

Author

Seiichi Manyama, Jun 29 2024

Status

approved