decompwlj 3D

Numbers not divisible by 2, 3 or 5

A007775 on the OEIS · family forced divisor · also known as Numbers coprime to 30

Weight–level plate of Numbers not divisible by 2, 3 or 5
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 viewerA007775 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L13,586 · 13.59 %
Weight class, k ≤ L86,412 · 86.41 %
Ties, k = L2
On the level line L = 14,002
Forced level, l ≤ d²4
Range of a(n)1 … 374,999
Range of the jump d2 … 6
Largest weight k, level L374,987, 124,999

Numbers prime to 2, 3 and 5. The gaps are 2, 4 and 6, repeating with period 8. The level class lies on only three lines: L = 3 (43 %), L = 1 and L = 5.

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.