decompwlj 3D

Numbers that contain odd digits only

A014261 on the OEIS · family digit rule · also known as Numbers with only odd digits

Weight–level plate of Numbers that contain odd 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 viewerA014261 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L17,403 · 17.40 %
Weight class, k ≤ L82,589 · 82.60 %
Ties, k = L15
On the level line L = 113,788
Forced level, l ≤ d²334
Range of a(n)1 … 11,177,779
Range of the jump d2 … 1,111,112
Largest weight k, level L11,177,773, 3,725,925

Every decimal digit odd. The gaps are 2, 12, 112, 1112, ... (80 % are 2). The level share is 17.40 %.

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.