decompwlj 3D

Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base

A060879 on the OEIS · family digit rule

Weight–level plate of Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
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 viewerA060879 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L59,942 · 59.94 %
Weight class, k ≤ L40,056 · 40.06 %
Ties, k = L8
On the level line L = 16,065
Forced level, l ≤ d²129
Range of a(n)257 … 243,848,342
Range of the jump d1 … 128,483
Largest weight k, level L243,388,759, 79,198,577

6,225 different gaps occur, from 1 to 128,483; the level share is 59.94 %.

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.