decompwlj 3D

Initial members of prime triples (p, p+2, p+14)

A350856 on the OEIS · family primes

Weight–level plate of Initial members of prime triples (p, p+2, p+14)
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 viewerA350856 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L61,068 · 61.07 %
Weight class, k ≤ L38,926 · 38.93 %
Ties, k = L0
On the level line L = 114,812
Forced level, l ≤ d²2,791
Range of a(n)3 … 156,173,579
Range of the jump d2 … 18,252
Largest weight k, level L156,156,467, 8,984,725

1,099 different gaps occur, from 2 to 18,252; the level share is 61.07 %; 2.8 % of terms are forced level (l <= d^2); there are no ties; 6 terms do not decompose.

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.