decompwlj 3D

a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digits

A016052 on the OEIS · family digit rule

Weight–level plate of a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digits
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 viewerA016052 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L14,676 · 14.68 %
Weight class, k ≤ L85,322 · 85.32 %
Ties, k = L4
On the level line L = 13
Forced level, l ≤ d²13
Range of a(n)3 … 2,662,359
Range of the jump d3 … 51
Largest weight k, level L295,703, 287,145

12 different gaps occur, from 3 to 51; the level share is 14.68 %; L = 9 holds 60 % 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.