decompwlj 3D

Numbers whose base-3 representation contains no 2

A005836 on the OEIS · family digit rule · also known as No digit 2 in base 3

Weight–level plate of Numbers whose base-3 representation contains no 2
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 viewerA005836 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,983
Level class, k > L14,744 · 14.75 %
Weight class, k ≤ L85,239 · 85.25 %
Ties, k = L0
On the level line L = 19,301
Forced level, l ≤ d²307
Range of a(n)0 … 57,476,668
Range of the jump d1 … 21,523,361
Largest weight k, level L57,475,421, 28,738,333

No digit 2 in base 3: the integers of the Cantor set, and the greedy sequence with no three terms in arithmetic progression. The gaps are (3^j + 1)/2 = 1, 2, 5, 14, ... Level share 14.75 %, and no ties.

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.