decompwlj 3D

a(n) = 3*n + 1

A016777 on the OEIS · family arithmetic progression · also known as 3n + 1

Weight–level plate of a(n) = 3*n + 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 viewerA016777 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,998
Level class, k > L19,911 · 19.91 %
Weight class, k ≤ L80,087 · 80.09 %
Ties, k = L100
On the level line L = 112,971
Forced level, l ≤ d²2
Range of a(n)1 … 299,998
Range of the jump d3 … 3
Largest weight k, level L299,983, 74,998

3n + 1: d = 3 and l = 3n - 2, prime to 3. The level share is about twice the multiples of 3's (9.60 %). The level share is 19.91 %; 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.