decompwlj 3D

Semiprimes of the form 4n + 1

A108181 on the OEIS · family multiplicative

Weight–level plate of Semiprimes of the form 4n + 1
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 viewerA108181 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L26,201 · 26.20 %
Weight class, k ≤ L73,798 · 73.80 %
Ties, k = L73
On the level line L = 111,387
Forced level, l ≤ d²19
Range of a(n)9 … 1,194,265
Range of the jump d4 … 96
Largest weight k, level L1,194,253, 238,833

24 different gaps occur, from 4 to 96; the level share is 26.20 %; L = 1 holds 43 % 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.