decompwlj 3D

Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4)

A016105 on the OEIS · family multiplicative

Weight–level plate of Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4)
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 viewerA016105 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L29,941 · 29.94 %
Weight class, k ≤ L70,057 · 70.06 %
Ties, k = L34
On the level line L = 112,907
Forced level, l ≤ d²26
Range of a(n)21 … 2,075,217
Range of the jump d4 … 244
Largest weight k, level L2,074,609, 415,017

44 different gaps occur, from 4 to 244; the level share is 29.94 %; 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.