decompwlj 3D

Fourth difference of fifth powers (A000584)

A101095 on the OEIS · family polynomial

Weight–level plate of Fourth difference of fifth powers (A000584)
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 viewerA101095 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L9,714 · 9.71 %
Weight class, k ≤ L90,282 · 90.29 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²119
Range of a(n)1 … 11,999,760
Range of the jump d27 … 120
Largest weight k, level L99,991, 99,120

The gaps are 27, 93, 119 and 120; the level share is 9.71 %; L = 120 holds 99 % 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.