decompwlj 3D

Numbers congruent to 11 mod 16

A106839 on the OEIS · family residue class

Weight–level plate of Numbers congruent to 11 mod 16
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 viewerA106839 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,998
Level class, k > L33,066 · 33.07 %
Weight class, k ≤ L66,932 · 66.93 %
Ties, k = L0
On the level line L = 115,151
Forced level, l ≤ d²15
Range of a(n)11 … 1,599,995
Range of the jump d16 … 16
Largest weight k, level L1,599,931, 94,107

The gap is always 16; the level share is 33.07 %; L = 1 holds 46 % 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.