A357019 a(n) is the largest possible x in n = x^2 - x*y + y^2 with integers x > y >= 0, or 0 if n cannot be expressed in this form.

0, 1, 0, 2, 2, 0, 0, 3, 0, 3, 0, 0, 4, 4, 0, 0, 4, 0, 0, 5, 0, 5, 0, 0, 0, 5, 0, 6, 6, 0, 0, 6, 0, 0, 0, 0, 6, 7, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 9, 0, 9, 8, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 10, 10, 0, 0, 10, 0, 9, 0, 0, 10, 0

Offset

0,4

Links

Table of n, a(n) for n=0..85.

Prog

(PARI) dloesch(n) = {my(L=List()); foreach([-1, 1], qs, my (D=qfbsolve(Qfb(1, qs, 1), factor(n), 3), dnp=#D); for (k=1, dnp, if(D[k][1]^2+D[k][2]^2-abs(D[k][1]*D[k][2])==n, listput (L, [abs(D[k][1]), abs(D[k][2])])))); Set(L)};
for (k=1, 85, my(D=dloesch(k), d=#D, m=0); for (j=1, d, m=max(m, D[j][1])); print1(m, ", "))
(Python)
from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A357019(n): return max((a for a, b in diop_quadratic(x*(x-y)+y**2-n)), default=0) # Chai Wah Wu, Sep 12 2022

Crossrefs

Cf. A002324, A003136, A133388.

Sequence in context: A158092 A145264 A300333 * A352562 A362326 A352909

Adjacent sequences: A357016 A357017 A357018 * A357020 A357021 A357022

Keyword

nonn

Author

Hugo Pfoertner, Sep 10 2022

Status

approved