decompwlj 3D

a(n+1) = a(n) + sum of digits in base 3 representation of a(n), with a(0) = 1

A010063 on the OEIS · family digit rule

Weight–level plate of a(n+1) = a(n) + sum of digits in base 3 representation of a(n), with a(0) = 1
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 viewerA010063 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,996
Level class, k > L22,314 · 22.31 %
Weight class, k ≤ L77,682 · 77.69 %
Ties, k = L1
On the level line L = 11
Forced level, l ≤ d²3
Range of a(n)1 … 1,245,146
Range of the jump d1 … 22
Largest weight k, level L622,513, 188,956

12 different gaps occur, from 1 to 22; the level share is 22.31 %; L = 2 holds 40 % 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.