decompwlj 3D

Numbers k such that 6*k+1, 12*k+1 and 18*k+1 are all primes

A046025 on the OEIS · family prime values

Weight–level plate of Numbers k such that 6*k+1, 12*k+1 and 18*k+1 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 viewerA046025 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L44,691 · 44.69 %
Weight class, k ≤ L55,305 · 55.31 %
Ties, k = L2
On the level line L = 15,773
Forced level, l ≤ d²482
Range of a(n)1 … 38,188,796
Range of the jump d1 … 4,810
Largest weight k, level L38,172,389, 18,541,352

1,503 different gaps occur, from 1 to 4,810; the level share is 44.69 %.

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.