decompwlj 3D

Prime numbers containing the string 13

A166573 on the OEIS · family primes

Weight–level plate of Prime numbers containing the string 13
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 viewerA166573 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L29,653 · 29.65 %
Weight class, k ≤ L70,343 · 70.35 %
Ties, k = L2
On the level line L = 16,719
Forced level, l ≤ d²657
Range of a(n)13 … 13,545,437
Range of the jump d2 … 4,006
Largest weight k, level L13,545,253, 4,515,093

609 different gaps occur, from 2 to 4,006; the level share is 29.65 %.

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.