decompwlj 3D

Strobogrammatic numbers: the same upside down

A000787 on the OEIS · family digit rule

Weight–level plate of Strobogrammatic numbers: the same upside down
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 viewerA000787 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,983
Level class, k > L93,375 · 93.39 %
Weight class, k ≤ L6,608 · 6.61 %
Ties, k = L0
On the level line L = 16,096
Forced level, l ≤ d²68,806
Range of a(n)0 … 86,000,000,000,098
Range of the jump d1 … 40,000,003,333,348
Largest weight k, level L69,998,589,986,669, 23,977,322

209 different gaps occur, from 1 to 40,000,003,333,348; the level share is 93.39 %; 68.8 % of terms are forced level (l <= d^2); there are no ties; 17 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.