decompwlj 3D

Numbers that have 4 terms in their Zeckendorf representation

A179244 on the OEIS · family digit rule

Weight–level plate of Numbers that have 4 terms in their Zeckendorf representation
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 viewerA179244 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L27,865 · 27.86 %
Weight class, k ≤ L72,135 · 72.14 %
Ties, k = L17
On the level line L = 16,090
Forced level, l ≤ d²5,657
Range of a(n)33 … 1,402,835,180
Range of the jump d1 … 24,157,829
Largest weight k, level L1,402,829,399, 701,417,589

132 different gaps occur, from 1 to 24,157,829; the level share is 27.86 %; 5.7 % of terms are forced level (l <= d^2).

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.