decompwlj 3D

Numbers that have only the straight digits {1, 4, 7}

A028373 on the OEIS · family digit rule

Weight–level plate of Numbers that have only the straight digits {1, 4, 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 viewerA028373 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,987
Level class, k > L18,020 · 18.02 %
Weight class, k ≤ L81,967 · 81.98 %
Ties, k = L1
On the level line L = 19,166
Forced level, l ≤ d²681
Range of a(n)1 … 11,471,711,171
Range of the jump d3 … 3,333,333,334
Largest weight k, level L11,471,477,711, 2,867,927,792

20 different gaps occur, from 3 to 3,333,333,334; the level share is 18.02 %; L = 1 holds 51 % of the level class; 13 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.