decompwlj 3D

Numbers without the decimal digits 3, 6 and 9

A307913 on the OEIS · family digit rule

Weight–level plate of Numbers without the decimal digits 3, 6 and 9
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 viewerA307913 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L11,476 · 11.48 %
Weight class, k ≤ L88,521 · 88.52 %
Ties, k = L15
On the level line L = 18,831
Forced level, l ≤ d²155
Range of a(n)0 … 785,475
Range of the jump d1 … 111,112
Largest weight k, level L785,423, 392,735

7 different gaps occur, from 1 to 111,112; the level share is 11.48 %; L = 1 holds 77 % 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.