decompwlj 3D

Primes of form 10*k + 9

A030433 on the OEIS · family primes · also known as Primes ending in 9

Weight–level plate of Primes of form 10*k + 9
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 viewerA030433 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L37,293 · 37.29 %
Weight class, k ≤ L62,705 · 62.71 %
Ties, k = L29
On the level line L = 19,828
Forced level, l ≤ d²57
Range of a(n)19 … 5,801,699
Range of the jump d10 … 510
Largest weight k, level L5,800,189, 527,139

Primes ending in 9. Every gap is a multiple of 10, so l ends in 9 and ties are possible. The level share is 37.29 %.

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.