decompwlj 3D

Numbers with rounded up arithmetic mean of digits = 1

A178361 on the OEIS · family digit rule

Weight–level plate of Numbers with rounded up arithmetic mean of digits = 1
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 viewerA178361 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L13,768 · 13.77 %
Weight class, k ≤ L86,223 · 86.23 %
Ties, k = L2
On the level line L = 15,108
Forced level, l ≤ d²1,898
Range of a(n)1 … 2,120,100,022
Range of the jump d1 … 100,000,000
Largest weight k, level L2,120,099,999, 1,060,050,010

73 different gaps occur, from 1 to 100,000,000; the level share is 13.77 %; 1.9 % of terms are forced level (l <= d^2); L = 1 holds 37 % of the level class; 9 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.