decompwlj 3D

Primes of the form 100*n+9

A166560 on the OEIS · family primes

Weight–level plate of Primes of the form 100*n+9
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 viewerA166560 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L53,237 · 53.24 %
Weight class, k ≤ L46,762 · 46.76 %
Ties, k = L20
On the level line L = 18,642
Forced level, l ≤ d²1,039
Range of a(n)109 … 67,972,609
Range of the jump d100 … 6,000
Largest weight k, level L67,961,209, 665,709

57 different gaps occur, from 100 to 6,000; the level share is 53.24 %; 1.0 % of terms are forced level (l <= d^2).

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.