decompwlj 3D

Primes of the form 2*3*5*7*n+79

A141563 on the OEIS · family primes

Weight–level plate of Primes of the form 2*3*5*7*n+79
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 viewerA141563 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L62,908 · 62.91 %
Weight class, k ≤ L37,090 · 37.09 %
Ties, k = L60
On the level line L = 124,318
Forced level, l ≤ d²1,259
Range of a(n)79 … 82,415,629
Range of the jump d210 … 7,770
Largest weight k, level L82,413,949, 389,419

33 different gaps occur, from 210 to 7,770; the level share is 62.91 %; 1.3 % of terms are forced level (l <= d^2); L = 1 holds 39 % 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.