decompwlj 3D

a(n) = 3*n

A008585 on the OEIS · family forced divisor · also known as Multiples of 3

Weight–level plate of a(n) = 3*n
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 viewerA008585 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,997
Level class, k > L9,595 · 9.60 %
Weight class, k ≤ L90,402 · 90.40 %
Ties, k = L1
On the level line L = 12
Forced level, l ≤ d²2
Range of a(n)0 … 299,997
Range of the jump d3 … 3
Largest weight k, level L99,991, 74,997

3n: d = 3 and l = 3(n - 1). The level class is essentially {3n : n - 1 prime}, all on the line L = 3, like the even numbers' line L = 2. The level share is 9.60 %.

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.