decompwlj 3D

Primes p such that p+4 and p+16 are also primes

A049492 on the OEIS · family primes

Weight–level plate of Primes p such that p+4 and p+16 are also 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 viewerA049492 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L65,864 · 65.87 %
Weight class, k ≤ L34,130 · 34.13 %
Ties, k = L7
On the level line L = 119,490
Forced level, l ≤ d²3,826
Range of a(n)3 … 203,958,577
Range of the jump d4 … 28,770
Largest weight k, level L203,941,909, 15,109,147

1,379 different gaps occur, from 4 to 28,770; the level share is 65.87 %; 3.8 % of terms are forced level (l <= d^2); 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.