decompwlj 3D

Palindromes in base 4 (written in base 10)

A014192 on the OEIS · family digit rule

Weight–level plate of Palindromes in base 4 (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 viewerA014192 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L83,203 · 83.21 %
Weight class, k ≤ L16,791 · 16.79 %
Ties, k = L8
On the level line L = 14,731
Forced level, l ≤ d²28,158
Range of a(n)0 … 2,258,635,410
Range of the jump d1 … 81,920
Largest weight k, level L1,073,676,287, 357,913,940

17 different gaps occur, from 1 to 81,920; the level share is 83.21 %; 28.2 % of terms are forced level (l <= d^2); 6 terms do not decompose.

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.