decompwlj 3D

Numbers such that all ten digits are needed to write all positive divisors in decimal representation

A095050 on the OEIS · family digit rule

Weight–level plate of Numbers such that all ten digits are needed to write all positive divisors 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 viewerA095050 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L14,313 · 14.31 %
Weight class, k ≤ L85,686 · 85.69 %
Ties, k = L7
On the level line L = 13,767
Forced level, l ≤ d²16
Range of a(n)108 … 282,356
Range of the jump d1 … 108
Largest weight k, level L282,287, 141,157

36 different gaps occur, from 1 to 108; the level share is 14.31 %; L = 2 holds 40 % 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.