decompwlj 3D

Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k)

A010070 on the OEIS · family digit rule

Weight–level plate of Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k)
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 viewerA010070 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L22,881 · 22.88 %
Weight class, k ≤ L77,115 · 77.12 %
Ties, k = L21
On the level line L = 17,875
Forced level, l ≤ d²9
Range of a(n)1 … 829,587
Range of the jump d2 … 46
Largest weight k, level L829,457, 276,506

6 different gaps occur, from 2 to 46; the level share is 22.88 %; L = 1 holds 34 % 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.