decompwlj 3D

a(n) = 3 * prime(n)

A001748 on the OEIS · family primes · also known as Three times the primes

Weight–level plate of a(n) = 3 * prime(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 viewerA001748 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L23,023 · 23.02 %
Weight class, k ≤ L76,974 · 76.98 %
Ties, k = L2
On the level line L = 13
Forced level, l ≤ d²28
Range of a(n)6 … 3,899,127
Range of the jump d3 … 342
Largest weight k, level L1,299,061, 556,875

3p. The level share is almost the primes' 23.00 %. The level share is 23.02 %; L = 3 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.