decompwlj 3D

Numbers with digitsum 13, in increasing order

A143164 on the OEIS · family digit rule

Weight–level plate of Numbers with digitsum 13, in increasing order
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 viewerA143164 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L30,901 · 30.90 %
Weight class, k ≤ L69,099 · 69.10 %
Ties, k = L3
On the level line L = 17,443
Forced level, l ≤ d²2,163
Range of a(n)49 … 111,032,122
Range of the jump d9 … 6,000,039
Largest weight k, level L111,032,113, 11,101,000

69 different gaps occur, from 9 to 6,000,039; the level share is 30.90 %; 2.2 % of terms are forced level (l <= d^2).

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.