decompwlj 3D

Contains digits 1 through 6 only

A057436 on the OEIS · family digit rule

Weight–level plate of Contains digits 1 through 6 only
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 viewerA057436 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L11,475 · 11.48 %
Weight class, k ≤ L88,517 · 88.52 %
Ties, k = L24
On the level line L = 19,590
Forced level, l ≤ d²150
Range of a(n)1 … 1,646,544
Range of the jump d1 … 444,445
Largest weight k, level L1,646,543, 823,271

7 different gaps occur, from 1 to 444,445; the level share is 11.48 %; L = 1 holds 84 % of the level class; 8 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.