decompwlj 3D

Primes having only {1, 2, 4} as digits

A260267 on the OEIS · family primes

Weight–level plate of Primes having only {1, 2, 4} 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 viewerA260267 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,975
Level class, k > L38,999 · 39.01 %
Weight class, k ≤ L60,976 · 60.99 %
Ties, k = L0
On the level line L = 15,881
Forced level, l ≤ d²3,325
Range of a(n)2 … 12,422,412,214,411
Range of the jump d9 … 6,666,666,669,970
Largest weight k, level L12,422,412,140,731, 1,129,192,929,291

3,993 different gaps occur, from 9 to 6,666,666,669,970; the level share is 39.01 %; 3.3 % 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.