decompwlj 3D

Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of k

A230092 on the OEIS · family binary rule

Weight–level plate of Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of k
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 viewerA230092 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L30,370 · 30.37 %
Weight class, k ≤ L69,629 · 69.63 %
Ties, k = L11
On the level line L = 16,592
Forced level, l ≤ d²197
Range of a(n)129 … 9,184,908
Range of the jump d2 … 252
Largest weight k, level L9,182,609, 3,058,009

20 different gaps occur, from 2 to 252; the level share is 30.37 %.

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.