decompwlj 3D

Numbers k such that k, 2*k+1, 3*k+2 are primes

A067256 on the OEIS · family primes

Weight–level plate of Numbers k such that k, 2*k+1, 3*k+2 are 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 viewerA067256 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L64,310 · 64.31 %
Weight class, k ≤ L35,685 · 35.69 %
Ties, k = L0
On the level line L = 115,526
Forced level, l ≤ d²4,426
Range of a(n)3 … 228,881,423
Range of the jump d2 … 32,004
Largest weight k, level L228,849,419, 32,660,141

1,539 different gaps occur, from 2 to 32,004; the level share is 64.31 %; 4.4 % of terms are forced level (l <= d^2); there are no ties.

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.