OFFSET
0,2
EXAMPLE
1 can't be written as 3*x*y^2 - x^3, so a(0) = 1.
3 * 1 * 1^2 - 1^3 = 2 so a(1) = 2.
3 * 2 * 4^2 - 2^3 = 3 * 8 * 5^2 - 8^3 = 88 so a(2) = 88.
3 * 4 * 8^2 - 4^3 = 3 * 16 * 10^2 - 16^3 = 3 * 64 * 37^2 - 64^3 = 704 so a(3) = 704.
3 * 6 * 45^2 - 6^3 = 3 * 9 * 37^2 - 9^3 = 3 * 33 * 27^2 - 33^3 = 3 * 549 * 317^2 - 549^3 = 36234 so a(4) = 36234.
3 * 9 * 103^2 - 9^3 = 3 * 33 * 57^2 - 33^3 = 3 * 78 * 57^2 - 78^3 = 3 * 333 * 193^2 - 333^3 = 3 * 1221 * 705^2 - 1221^3 = 285714 so a(5) = 285714.
MAPLE
N:= 3*10^5: # for terms <= N
R:= Vector(N):
for x from 1 to floor(N/2) do
V:= [seq(3*x*y^2 - x^3, y = ceil(x/sqrt(3)) .. floor(sqrt((x^2+N/x)/3)))];
R[V]:= R[V] +~ 1;
od:
W:= Array(0..max(R)):
for i from 1 to N do
v:= R[i];
if W[v] = 0 then W[v]:= i fi
od:
convert(W, list);
MATHEMATICA
NVal = 2285712; R = ConstantArray[0, NVal]; For[x = 1, x <= Floor[NVal/2], x++, V = Table[3*x*y^2 - x^3, {y, Ceiling[x/Sqrt[3]], Floor[Sqrt[x^2 + NVal/x]/Sqrt[3]]}]; R[[V]] = R[[V]] + 1; ]; W = ConstantArray[0, Max[R] + 1]; For[i = 1, i <= NVal, i++, v = R[[i]]; If[W[[v + 1]] == 0, W[[v + 1]] = i]; ]; W (* Robert P. P. McKone, Aug 18 2023 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Aug 14 2023
EXTENSIONS
a(6)-a(7) from Giorgos Kalogeropoulos, Aug 18 2023
STATUS
approved