decompwlj 3D

Multiples of 21

A008603 on the OEIS · family residue class

Weight–level plate of Multiples of 21
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 viewerA008603 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,997
Level class, k > L9,620 · 9.62 %
Weight class, k ≤ L90,377 · 90.38 %
Ties, k = L0
On the level line L = 12
Forced level, l ≤ d²20
Range of a(n)0 … 2,099,979
Range of the jump d21 … 21
Largest weight k, level L99,991, 95,445

The gap is always 21; the level share is 9.62 %; L = 21 holds 100 % of the level class; there are no ties.

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.