decompwlj 3D

Primes having only {0, 2, 3} as digits

A260125 on the OEIS · family primes

Weight–level plate of Primes having only {0, 2, 3} 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 viewerA260125 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,986
Level class, k > L37,534 · 37.54 %
Weight class, k ≤ L62,452 · 62.46 %
Ties, k = L0
On the level line L = 15,866
Forced level, l ≤ d²2,688
Range of a(n)2 … 30,230,232,323,303
Range of the jump d1 … 16,666,666,670,080
Largest weight k, level L30,230,230,301,723, 2,748,202,756,383

4,114 different gaps occur, from 1 to 16,666,666,670,080; the level share is 37.54 %; 2.7 % of terms are forced level (l <= d^2); there are no ties; 14 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.