decompwlj 3D

Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits

A061426 on the OEIS · family digit rule

Weight–level plate of Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits
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 viewerA061426 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,987
Level class, k > L26,849 · 26.85 %
Weight class, k ≤ L73,138 · 73.15 %
Ties, k = L0
On the level line L = 14,810
Forced level, l ≤ d²1,884
Range of a(n)2 … 12,414,121,244
Range of the jump d6 … 3,227,000,177
Largest weight k, level L12,412,821,203, 1,773,202,016

196 different gaps occur, from 6 to 3,227,000,177; the level share is 26.85 %; 1.9 % of terms are forced level (l <= d^2); there are no ties; 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.