decompwlj 3D

Nonnegative numbers that are palindromes in balanced ternary representation

A134027 on the OEIS · family digit rule

Weight–level plate of Nonnegative numbers that are palindromes in balanced ternary 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 viewerA134027 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L93,805 · 93.81 %
Weight class, k ≤ L6,191 · 6.19 %
Ties, k = L14
On the level line L = 17,238
Forced level, l ≤ d²65,483
Range of a(n)0 … 4,161,464,959
Range of the jump d1 … 78,732
Largest weight k, level L4,158,671,431, 116,226,146

20 different gaps occur, from 1 to 78,732; the level share is 93.81 %; 65.5 % 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.