decompwlj 3D

Primes having only {7, 8, 9} as digits

A106110 on the OEIS · family primes

Weight–level plate of Primes having only {7, 8, 9} 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 viewerA106110 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,988
Level class, k > L28,168 · 28.17 %
Weight class, k ≤ L71,820 · 71.83 %
Ties, k = L1
On the level line L = 14,330
Forced level, l ≤ d²1,125
Range of a(n)7 … 8,899,899,777,799
Range of the jump d2 … 6,777,777,777,890
Largest weight k, level L8,899,898,977,799, 2,966,632,929,925

1,275 different gaps occur, from 2 to 6,777,777,777,890; the level share is 28.17 %; 1.1 % of terms are forced level (l <= d^2); 12 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.