decompwlj 3D

Primes of the form 10*n+1

A030430 on the OEIS · family primes · also known as Primes ending in 1

Weight–level plate of Primes of the form 10*n+1
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 viewerA030430 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L37,200 · 37.20 %
Weight class, k ≤ L62,799 · 62.80 %
Ties, k = L22
On the level line L = 19,767
Forced level, l ≤ d²62
Range of a(n)11 … 5,803,411
Range of the jump d10 … 500
Largest weight k, level L5,803,351, 526,461

Primes ending in 1. Every gap is a multiple of 10, so l ends in 1 as well. The level share is 37.20 %.

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.