decompwlj 3D

n is divisible by |(product of digits) - (sum of digits)|

A038368 on the OEIS · family digit rule

Weight–level plate of n is divisible by |(product of digits) - (sum of 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 viewerA038368 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L19,451 · 19.45 %
Weight class, k ≤ L80,549 · 80.55 %
Ties, k = L4
On the level line L = 12,118
Forced level, l ≤ d²20
Range of a(n)10 … 1,703,060
Range of the jump d1 … 180
Largest weight k, level L1,702,823, 851,300

130 different gaps occur, from 1 to 180; the level share is 19.45 %.

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.