decompwlj 3D

Primes having only {3, 4, 8} as digits

A199348 on the OEIS · family primes

Weight–level plate of Primes having only {3, 4, 8} as 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 viewerA199348 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,975
Level class, k > L39,602 · 39.61 %
Weight class, k ≤ L60,373 · 60.39 %
Ties, k = L0
On the level line L = 15,736
Forced level, l ≤ d²3,211
Range of a(n)3 … 38,334,344,833,333
Range of the jump d10 … 24,444,444,460,550
Largest weight k, level L38,334,334,423,223, 3,484,858,044,393

3,287 different gaps occur, from 10 to 24,444,444,460,550; the level share is 39.61 %; 3.2 % of terms are forced level (l <= d^2); there are no ties; 25 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.