decompwlj 3D

Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digit

A256634 on the OEIS · family digit rule

Weight–level plate of Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digit
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 viewerA256634 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L22,185 · 22.19 %
Weight class, k ≤ L77,814 · 77.81 %
Ties, k = L2
On the level line L = 14,440
Forced level, l ≤ d²993
Range of a(n)740 … 37,032,515
Range of the jump d1 … 3,847,500
Largest weight k, level L37,032,497, 18,516,252

2,033 different gaps occur, from 1 to 3,847,500; the level share is 22.19 %.

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.