decompwlj 3D

a(2n) = 3*a(n), a(2n+1) = 2*a(n+1)+a(n), with a(1) = 1

A064194 on the OEIS · family self-referential

Weight–level plate of a(2n) = 3*a(n), a(2n+1) = 2*a(n+1)+a(n), with a(1) = 1
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 viewerA064194 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L56,699 · 56.70 %
Weight class, k ≤ L43,297 · 43.30 %
Ties, k = L16
On the level line L = 118,097
Forced level, l ≤ d²3,372
Range of a(n)1 … 105,823,341
Range of the jump d2 … 131,072
Largest weight k, level L105,809,773, 8,609,339

17 different gaps occur, from 2 to 131,072; the level share is 56.70 %; 3.4 % of terms are forced level (l <= d^2); L = 1 holds 32 % of the level class.

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.