decompwlj 3D

Primes having only {3, 4, 7} as digits

A199347 on the OEIS · family primes

Weight–level plate of Primes having only {3, 4, 7} 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 viewerA199347 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,976
Level class, k > L33,776 · 33.78 %
Weight class, k ≤ L66,200 · 66.22 %
Ties, k = L0
On the level line L = 16,327
Forced level, l ≤ d²2,137
Range of a(n)3 … 4,477,734,334,433
Range of the jump d4 … 2,555,555,555,574
Largest weight k, level L4,477,477,777,417, 639,639,635,333

3,637 different gaps occur, from 4 to 2,555,555,555,574; the level share is 33.78 %; 2.1 % of terms are forced level (l <= d^2); there are no ties; 24 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.