decompwlj 3D

Numbers using only digits 1 and 7

A276039 on the OEIS · family digit rule

Weight–level plate of Numbers using only digits 1 and 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 viewerA276039 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,982
Level class, k > L17,227 · 17.23 %
Weight class, k ≤ L82,755 · 82.77 %
Ties, k = L0
On the level line L = 13,717
Forced level, l ≤ d²1,135
Range of a(n)1 … 7,111,177,171,711,117
Range of the jump d4 … 5,333,333,333,333,334
Largest weight k, level L7,111,177,171,106,443, 1,015,882,453,025,395

31 different gaps occur, from 4 to 5,333,333,333,333,334; the level share is 17.23 %; 1.1 % of terms are forced level (l <= d^2); there are no ties; 18 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.