decompwlj 3D

Numbers n such that 107*n - 109 is prime

A107406 on the OEIS · family prime values

Weight–level plate of Numbers n such that 107*n - 109 is prime
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 viewerA107406 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L24,143 · 24.14 %
Weight class, k ≤ L75,857 · 75.86 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²20
Range of a(n)24 … 1,782,960
Range of the jump d2 … 192
Largest weight k, level L891,377, 445,598

73 different gaps occur, from 2 to 192; the level share is 24.14 %; L = 2 holds 41 % 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.