decompwlj 3D

Semiprimes sandwiched between semiprimes

A086005 on the OEIS · family multiplicative

Weight–level plate of Semiprimes sandwiched between semiprimes
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 viewerA086005 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L50,000 · 50.00 %
Weight class, k ≤ L49,999 · 50.00 %
Ties, k = L0
On the level line L = 13
Forced level, l ≤ d²1,537
Range of a(n)34 … 96,015,922
Range of the jump d4 … 13,404
Largest weight k, level L48,003,013, 17,573,010

1,510 different gaps occur, from 4 to 13,404; the level share is 50.00 %; 1.5 % 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.