decompwlj 3D

Palindromes in base 3 (written in base 10)

A014190 on the OEIS · family digit rule

Weight–level plate of Palindromes in base 3 (written in base 10)
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 viewerA014190 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L84,185 · 84.19 %
Weight class, k ≤ L15,811 · 15.81 %
Ties, k = L12
On the level line L = 13,156
Forced level, l ≤ d²32,413
Range of a(n)0 … 2,418,140,684
Range of the jump d1 … 78,732
Largest weight k, level L1,161,957,473, 387,420,488

21 different gaps occur, from 1 to 78,732; the level share is 84.19 %; 32.4 % 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.