decompwlj 3D

Palindromic in base 9

A029955 on the OEIS · family digit rule

Weight–level plate of Palindromic in base 9
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 viewerA029955 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L79,549 · 79.55 %
Weight class, k ≤ L20,446 · 20.45 %
Ties, k = L13
On the level line L = 13,316
Forced level, l ≤ d²36,574
Range of a(n)0 … 2,418,125,910
Range of the jump d1 … 65,610
Largest weight k, level L387,341,027, 129,140,162

11 different gaps occur, from 1 to 65,610; the level share is 79.55 %; 36.6 % 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.