decompwlj 3D

Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base

A060947 on the OEIS · family digit rule

Weight–level plate of Intrinsic 10-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 viewerA060947 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L82,336 · 82.34 %
Weight class, k ≤ L17,661 · 17.66 %
Ties, k = L2
On the level line L = 12,523
Forced level, l ≤ d²49,006
Range of a(n)513 … 2,359,331,070
Range of the jump d1 … 904,551
Largest weight k, level L1,999,868,329, 263,063,389

23,256 different gaps occur, from 1 to 904,551; the level share is 82.34 %; 49.0 % 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.