decompwlj 3D

Numbers in which all digits are neither primes nor zero, i.e., are members of (1, 4, 6, 8, 9)

A202268 on the OEIS · family digit rule

Weight–level plate of Numbers in which all digits are neither primes nor zero, i.e., are members of (1, 4, 6, 8, 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 viewerA202268 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L15,836 · 15.84 %
Weight class, k ≤ L84,156 · 84.16 %
Ties, k = L0
On the level line L = 16,893
Forced level, l ≤ d²303
Range of a(n)1 … 11,188,889
Range of the jump d1 … 2,111,112
Largest weight k, level L11,188,657, 3,729,629

15 different gaps occur, from 1 to 2,111,112; the level share is 15.84 %; L = 1 holds 44 % of the level class; there are no ties; 8 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.