decompwlj 3D

Primes without positive even digits

A155055 on the OEIS · family primes

Weight–level plate of Primes without positive even digits
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 viewerA155055 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L27,164 · 27.17 %
Weight class, k ≤ L72,827 · 72.83 %
Ties, k = L9
On the level line L = 16,552
Forced level, l ≤ d²813
Range of a(n)3 … 55,053,311
Range of the jump d2 … 10,000,038
Largest weight k, level L55,050,001, 18,350,363

445 different gaps occur, from 2 to 10,000,038; the level share is 27.17 %; 9 terms do not decompose.

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.