decompwlj 3D

Beatty sequence for log(3)/(log(3)-1)

A059544 on the OEIS · family Beatty

Weight–level plate of Beatty sequence for log(3)/(log(3)-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 viewerA059544 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L25,732 · 25.73 %
Weight class, k ≤ L74,266 · 74.27 %
Ties, k = L19
On the level line L = 17,740
Forced level, l ≤ d²10
Range of a(n)11 … 1,114,072
Range of the jump d11 … 12
Largest weight k, level L1,114,039, 92,831

The gaps are 11 and 12; the level share is 25.73 %; L = 1 holds 30 % 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.