decompwlj 3D

Strictly non-palindromic numbers: n is not palindromic in any base b with 2 <= b <= n-2

A016038 on the OEIS · family digit rule

Weight–level plate of Strictly non-palindromic numbers: n is not palindromic in any base b with 2 <= b <= n-2
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 viewerA016038 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,993
Level class, k > L43,098 · 43.10 %
Weight class, k ≤ L56,895 · 56.90 %
Ties, k = L8
On the level line L = 18,086
Forced level, l ≤ d²253
Range of a(n)0 … 25,947,539
Range of the jump d1 … 3,834
Largest weight k, level L25,946,611, 8,620,873

953 different gaps occur, from 1 to 3,834; the level share is 43.10 %; 7 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.