decompwlj 3D

The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3))

A007412 on the OEIS · family complement · also known as Non-cubes

Weight–level plate of The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3))
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA007412 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L9,600 · 9.60 %
Weight class, k ≤ L90,399 · 90.40 %
Ties, k = L64
On the level line L = 19,598
Forced level, l ≤ d²0
Range of a(n)2 … 100,046
Range of the jump d1 … 2
Largest weight k, level L100,043, 50,022

Not a cube. Gaps 1, and 2 across each cube: the naturals' plane. The level share is 9.60 %; L = 1 holds 100 % of the level class.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.