decompwlj 3D

a(n+1) = 2a(n) - {largest prime < a(n)}

A033556 on the OEIS · family primes

Weight–level plate of a(n+1) = 2a(n) - {largest prime < a(n)}
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 viewerA033556 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)100,000
Level class, k > L100,000 · 100.00 %
Weight class, k ≤ L0 · 0.00 %
Ties, k = L0
On the level line L = 1100,000
Forced level, l ≤ d²3
Range of a(n)3 … 849,257
Range of the jump d1 … 96
Largest weight k, level L849,253, 1

30 different gaps occur, from 1 to 96; the level share is 100.00 %; L = 1 holds 100 % of the level class; there are no ties.

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.