decompwlj 3D

Numbers that are palindromic in base 14

A029959 on the OEIS · family digit rule

Weight–level plate of Numbers that are palindromic in base 14
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 viewerA029959 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L83,434 · 83.44 %
Weight class, k ≤ L16,561 · 16.56 %
Ties, k = L21
On the level line L = 14,705
Forced level, l ≤ d²36,079
Range of a(n)0 … 2,365,817,721
Range of the jump d1 … 41,160
Largest weight k, level L2,365,238,737, 59,581,545

10 different gaps occur, from 1 to 41,160; the level share is 83.44 %; 36.1 % 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.