decompwlj 3D

Primes that remain prime through 2 iterations of function f(x) = x + 6

A023241 on the OEIS · family primes

Weight–level plate of Primes that remain prime through 2 iterations of function f(x) = x + 6
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 viewerA023241 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L49,134 · 49.14 %
Weight class, k ≤ L50,862 · 50.86 %
Ties, k = L2
On the level line L = 16,617
Forced level, l ≤ d²1,530
Range of a(n)5 … 88,681,277
Range of the jump d2 … 11,774
Largest weight k, level L88,669,627, 12,657,845

1,781 different gaps occur, from 2 to 11,774; the level share is 49.14 %; 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.