decompwlj 3D

Numbers with exactly two distinct decimal digits, neither of which is 0

A101594 on the OEIS · family digit rule

Weight–level plate of Numbers with exactly two distinct decimal digits, neither of which is 0
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 viewerA101594 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L22,598 · 22.60 %
Weight class, k ≤ L77,402 · 77.40 %
Ties, k = L6
On the level line L = 15,206
Forced level, l ≤ d²3,808
Range of a(n)12 … 44,424,224,444
Range of the jump d1 … 1,111,111,114
Largest weight k, level L44,414,438,777, 22,172,222,221

131 different gaps occur, from 1 to 1,111,111,114; the level share is 22.60 %; 3.8 % of terms are forced level (l <= d^2).

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.