decompwlj 3D

a(n) = 3*n + 2

A016789 on the OEIS · family arithmetic progression · also known as 3n + 2

Weight–level plate of a(n) = 3*n + 2
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 viewerA016789 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,998
Level class, k > L19,932 · 19.93 %
Weight class, k ≤ L80,066 · 80.07 %
Ties, k = L0
On the level line L = 113,025
Forced level, l ≤ d²2
Range of a(n)2 … 299,999
Range of the jump d3 … 3
Largest weight k, level L299,993, 74,999

3n + 2: d = 3 and l = 3n - 1 = 2 (mod 3), never a square: no ties, by proof. The level share is 19.93 %; L = 1 holds 65 % 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.