decompwlj 3D

Two iterations of Reverse and Add are needed to reach a palindrome

A015977 on the OEIS · family digit rule

Weight–level plate of Two iterations of Reverse and Add are needed to reach a palindrome
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 viewerA015977 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,999
Level class, k > L13,012 · 13.01 %
Weight class, k ≤ L86,987 · 86.99 %
Ties, k = L32
On the level line L = 18,412
Forced level, l ≤ d²96
Range of a(n)5 … 547,395
Range of the jump d1 … 540
Largest weight k, level L547,387, 273,697

120 different gaps occur, from 1 to 540; the level share is 13.01 %; L = 1 holds 65 % of the level class.

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.