OFFSET
1,1
COMMENTS
Conjecture: The sequence has totally 150 terms as listed in the b-file the largest of which is 182842. Thus any integer n > 182842 can be written as x^3 + 3*y^2 + z^2 with x,y,z nonnegative integers.
We note that the sequence has no term greater than 182842 and not exceeding 10^6.
See also A275169 for a similar conjecture.
It is known that for any positive integers a,b,c there are infinitely many positive integers not of the form a*x^2 + b*y^2 + c*z^2 with x,y,z nonnegative integers.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..150
EXAMPLE
a(1) = 6 since 1 = 0^3 + 3*0^2 + 1^2, 2 = 1^3 + 3*0^2 + 1^2, 3 = 0^3 + 3*1^2 + 0^2, 4 = 0^3 + 3*1^2 + 1^2, 5 = 1^3 + 3*1^2 + 1^2, but 6 cannot be written as x^3 + 3*y^2 + z^2 with x,y,z nonnegative integers.
MATHEMATICA
SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
n=0; Do[Do[If[SQ[m-x^3-3*y^2], Goto[aa]], {x, 0, m^(1/3)}, {y, 0, Sqrt[(m-x^3)/3]}]; n=n+1; Print[n, " ", m]; Label[aa]; Continue, {m, 1, 1800}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jul 18 2016
STATUS
approved