decompwlj 3D

Primes p such that 3*p-4, 3*p-10, and 3*p-14 are all prime

A230223 on the OEIS · family primes

Weight–level plate of Primes p such that 3*p-4, 3*p-10, and 3*p-14 are all prime
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 viewerA230223 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L65,464 · 65.47 %
Weight class, k ≤ L34,533 · 34.53 %
Ties, k = L3
On the level line L = 18,006
Forced level, l ≤ d²9,118
Range of a(n)7 … 442,641,539
Range of the jump d2 … 65,620
Largest weight k, level L442,606,807, 146,966,825

9,201 different gaps occur, from 2 to 65,620; the level share is 65.47 %; 9.1 % 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.