decompwlj 3D

Primes written in base 6

A004680 on the OEIS · family digit rule

Weight–level plate of Primes written in base 6
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 viewerA004680 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L30,656 · 30.66 %
Weight class, k ≤ L69,335 · 69.34 %
Ties, k = L5
On the level line L = 111,709
Forced level, l ≤ d²619
Range of a(n)2 … 43,505,101
Range of the jump d1 … 4,444,510
Largest weight k, level L43,504,151, 6,207,201

238 different gaps occur, from 1 to 4,444,510; the level share is 30.66 %; L = 1 holds 38 % of the level class; 9 terms do not decompose.

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.