decompwlj 3D

Palindromic in base 5

A029952 on the OEIS · family digit rule

Weight–level plate of Palindromic in base 5
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 viewerA029952 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L78,443 · 78.45 %
Weight class, k ≤ L21,551 · 21.55 %
Ties, k = L12
On the level line L = 14,155
Forced level, l ≤ d²18,879
Range of a(n)0 … 1,708,984,386
Range of the jump d1 … 93,750
Largest weight k, level L1,220,299,999, 71,806,066

15 different gaps occur, from 1 to 93,750; the level share is 78.45 %; 18.9 % of terms are forced level (l <= d^2); 6 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.