decompwlj 3D

Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base

A060874 on the OEIS · family digit rule

Weight–level plate of Intrinsic 4-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 viewerA060874 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L29,216 · 29.22 %
Weight class, k ≤ L70,782 · 70.78 %
Ties, k = L3
On the level line L = 13,314
Forced level, l ≤ d²32
Range of a(n)9 … 5,340,621
Range of the jump d1 … 647
Largest weight k, level L5,337,791, 2,667,172

434 different gaps occur, from 1 to 647; the level share is 29.22 %.

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.