decompwlj 3D

Numbers k such that k-6, k, and k+6 are primes

A006489 on the OEIS · family primes

Weight–level plate of Numbers k such that k-6, k, and k+6 are 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 viewerA006489 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L60,472 · 60.47 %
Weight class, k ≤ L39,526 · 39.53 %
Ties, k = L4
On the level line L = 117,989
Forced level, l ≤ d²1,530
Range of a(n)11 … 88,681,283
Range of the jump d2 … 11,774
Largest weight k, level L88,676,447, 8,067,791

1,781 different gaps occur, from 2 to 11,774; the level share is 60.47 %; 1.5 % of terms are forced level (l <= d^2).

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.