decompwlj 3D

Primes for which the level is equal to 1 in A117563

A125830 on the OEIS · family primes

Weight–level plate of Primes for which the level is equal to 1 in A117563
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 viewerA125830 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L49,846 · 49.85 %
Weight class, k ≤ L50,149 · 50.15 %
Ties, k = L4
On the level line L = 116,172
Forced level, l ≤ d²368
Range of a(n)5 … 25,366,591
Range of the jump d6 … 3,756
Largest weight k, level L25,364,897, 2,806,435

952 different gaps occur, from 6 to 3,756; the level share is 49.85 %; 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.