decompwlj 3D

Numbers k with digits 5 and 7 only

A284380 on the OEIS · family digit rule

Weight–level plate of Numbers k with digits 5 and 7 only
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 viewerA284380 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,985
Level class, k > L15,302 · 15.30 %
Weight class, k ≤ L84,683 · 84.70 %
Ties, k = L0
On the level line L = 17,615
Forced level, l ≤ d²629
Range of a(n)5 … 7,555,577,575,755,557
Range of the jump d2 … 4,777,777,777,777,778
Largest weight k, level L7,555,577,575,575,539, 2,518,525,858,525,851

31 different gaps occur, from 2 to 4,777,777,777,777,778; the level share is 15.30 %; L = 1 holds 50 % of the level class; there are no ties; 15 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.