decompwlj 3D

Numbers that are the sum of 9 consecutive primes

A127336 on the OEIS · family primes

Weight–level plate of Numbers that are the sum of 9 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 viewerA127336 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L45,889 · 45.89 %
Weight class, k ≤ L54,111 · 54.11 %
Ties, k = L16
On the level line L = 113,173
Forced level, l ≤ d²66
Range of a(n)100 … 11,698,003
Range of the jump d27 … 300
Largest weight k, level L11,696,071, 210,633

124 different gaps occur, from 27 to 300; the level share is 45.89 %.

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.