decompwlj 3D

Primes with maximal digit > 7

A106124 on the OEIS · family primes

Weight–level plate of Primes with maximal digit > 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 viewerA106124 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L24,691 · 24.69 %
Weight class, k ≤ L75,307 · 75.31 %
Ties, k = L15
On the level line L = 17,596
Forced level, l ≤ d²27
Range of a(n)19 … 1,828,831
Range of the jump d2 … 340
Largest weight k, level L1,828,691, 609,609

111 different gaps occur, from 2 to 340; the level share is 24.69 %; L = 1 holds 31 % of the level class.

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.