decompwlj 3D

Numbers that are the sum of 10 consecutive primes

A127337 on the OEIS · family primes

Weight–level plate of Numbers that are the sum of 10 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 viewerA127337 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L37,634 · 37.63 %
Weight class, k ≤ L62,366 · 62.37 %
Ties, k = L1
On the level line L = 10
Forced level, l ≤ d²77
Range of a(n)129 … 12,997,836
Range of the jump d29 … 306
Largest weight k, level L6,498,353, 235,596

127 different gaps occur, from 29 to 306; the level share is 37.63 %.

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.