decompwlj 3D

Numbers k such that k is a product of two primes and k-2 is prime

A062721 on the OEIS · family multiplicative

Weight–level plate of Numbers k such that k is a product of two primes and k-2 is 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 viewerA062721 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L40,231 · 40.23 %
Weight class, k ≤ L59,767 · 59.77 %
Ties, k = L23
On the level line L = 119,223
Forced level, l ≤ d²41
Range of a(n)4 … 5,633,761
Range of the jump d4 … 626
Largest weight k, level L5,633,149, 1,125,241

220 different gaps occur, from 4 to 626; the level share is 40.23 %; L = 1 holds 48 % of the level class.

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.