decompwlj 3D

Palindromic in base 7

A029954 on the OEIS · family digit rule

Weight–level plate of Palindromic in base 7
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 viewerA029954 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L77,064 · 77.07 %
Weight class, k ≤ L22,931 · 22.93 %
Ties, k = L24
On the level line L = 14,583
Forced level, l ≤ d²15,144
Range of a(n)0 … 1,398,238,027
Range of the jump d1 … 19,208
Largest weight k, level L1,397,844,263, 62,772,276

12 different gaps occur, from 1 to 19,208; the level share is 77.07 %; 15.1 % 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.