decompwlj 3D

Digits are cubes

A046031 on the OEIS · family digit rule

Weight–level plate of Digits are cubes
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 viewerA046031 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,979
Level class, k > L15,764 · 15.77 %
Weight class, k ≤ L84,215 · 84.23 %
Ties, k = L2
On the level line L = 13,868
Forced level, l ≤ d²518
Range of a(n)0 … 18,008,011,800
Range of the jump d1 … 6,111,111,112
Largest weight k, level L18,008,011,079, 6,002,670,393

21 different gaps occur, from 1 to 6,111,111,112; the level share is 15.77 %; 21 terms do not decompose.

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.