decompwlj 3D

Numbers that are the sum of 11 consecutive primes

A127338 on the OEIS · family primes

Weight–level plate of Numbers that are the sum of 11 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 viewerA127338 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L47,365 · 47.37 %
Weight class, k ≤ L52,635 · 52.63 %
Ties, k = L12
On the level line L = 113,030
Forced level, l ≤ d²83
Range of a(n)160 … 14,297,677
Range of the jump d35 … 318
Largest weight k, level L14,296,657, 220,919

134 different gaps occur, from 35 to 318; the level share is 47.37 %.

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.