decompwlj 3D

Prime p such that p, p+10, p+12 are all primes

A212492 on the OEIS · family primes

Weight–level plate of Prime p such that p, p+10, p+12 are all 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 viewerA212492 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L59,029 · 59.03 %
Weight class, k ≤ L40,967 · 40.97 %
Ties, k = L12
On the level line L = 115,253
Forced level, l ≤ d²2,069
Range of a(n)7 … 124,603,267
Range of the jump d6 … 16,794
Largest weight k, level L124,600,363, 17,723,725

1,390 different gaps occur, from 6 to 16,794; the level share is 59.03 %; 2.1 % 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.