decompwlj 3D

Primes that are the sum of 7 consecutive primes

A082246 on the OEIS · family primes

Weight–level plate of Primes that are the sum of 7 consecutive primes
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 viewerA082246 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L52,371 · 52.37 %
Weight class, k ≤ L47,629 · 47.63 %
Ties, k = L2
On the level line L = 18,253
Forced level, l ≤ d²1,434
Range of a(n)197 … 86,412,433
Range of the jump d26 … 12,782
Largest weight k, level L86,411,509, 1,637,965

2,607 different gaps occur, from 26 to 12,782; the level share is 52.37 %; 1.4 % of terms are forced level (l <= d^2).

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.