decompwlj 3D

Numbers that contain even digits only

A014263 on the OEIS · family digit rule · also known as Only even digits

Weight–level plate of Numbers that contain even digits 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 viewerA014263 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,990
Level class, k > L11,078 · 11.08 %
Weight class, k ≤ L88,912 · 88.92 %
Ties, k = L3
On the level line L = 17
Forced level, l ≤ d²278
Range of a(n)0 … 22,288,888
Range of the jump d2 … 11,111,112
Largest weight k, level L11,144,429, 7,429,628

Every decimal digit even. The gaps are 2, 12, 112, ..., as for the only-odd-digit numbers. The level share is 11.08 %; L = 2 holds 63 % 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.