decompwlj 3D

Sums of four consecutive primes

A034963 on the OEIS · family primes

Weight–level plate of Sums of four 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 viewerA034963 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L31,418 · 31.42 %
Weight class, k ≤ L68,581 · 68.58 %
Ties, k = L1
On the level line L = 12
Forced level, l ≤ d²28
Range of a(n)17 … 5,198,936
Range of the jump d9 … 180
Largest weight k, level L2,599,427, 383,496

82 different gaps occur, from 9 to 180; the level share is 31.42 %.

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.