decompwlj 3D

Numbers containing only digits 3 or 7 in decimal representation

A143967 on the OEIS · family digit rule

Weight–level plate of Numbers containing only digits 3 or 7 in decimal representation
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 viewerA143967 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,969
Level class, k > L17,946 · 17.95 %
Weight class, k ≤ L82,023 · 82.05 %
Ties, k = L0
On the level line L = 17,465
Forced level, l ≤ d²867
Range of a(n)3 … 7,333,377,373,733,337
Range of the jump d4 … 3,555,555,555,555,556
Largest weight k, level L7,333,377,337,777,769, 1,047,625,339,053,967

31 different gaps occur, from 4 to 3,555,555,555,555,556; the level share is 17.95 %; L = 1 holds 42 % of the level class; there are no ties; 31 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.