decompwlj 3D

Primes written in base 7

A004681 on the OEIS · family digit rule

Weight–level plate of Primes written 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 viewerA004681 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L23,622 · 23.62 %
Weight class, k ≤ L76,369 · 76.38 %
Ties, k = L2
On the level line L = 14,027
Forced level, l ≤ d²499
Range of a(n)2 … 14,022,145
Range of the jump d1 … 3,333,339
Largest weight k, level L14,021,317, 4,673,774

305 different gaps occur, from 1 to 3,333,339; the level share is 23.62 %; 9 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.