decompwlj 3D

Primes of the form p*q + p - q, where p and q are distinct primes

A091301 on the OEIS · family primes

Weight–level plate of Primes of the form p*q + p - q, where p and q are distinct 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 viewerA091301 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L32,678 · 32.68 %
Weight class, k ≤ L67,320 · 67.32 %
Ties, k = L52
On the level line L = 111,304
Forced level, l ≤ d²21
Range of a(n)5 … 3,868,021
Range of the jump d2 … 408
Largest weight k, level L3,867,679, 1,288,325

152 different gaps occur, from 2 to 408; the level share is 32.68 %; L = 1 holds 35 % 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.