decompwlj 3D

Numbers that are the sum of 2 successive primes

A001043 on the OEIS · family primes · also known as Sums of two successive primes

Weight–level plate of Numbers that are the sum of 2 successive 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 viewerA001043 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L24,897 · 24.90 %
Weight class, k ≤ L75,100 · 75.10 %
Ties, k = L1
On the level line L = 11
Forced level, l ≤ d²15
Range of a(n)5 … 2,599,430
Range of the jump d3 … 138
Largest weight k, level L1,299,637, 366,234

p(n) + p(n+1), all even past the first term. l is even, and the line L = 1 holds a single term. The level share is 24.90 %.

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.