decompwlj 3D

Primes whose digits are composite; primes having only {4, 6, 8, 9} as digits

A051416 on the OEIS · family primes

Weight–level plate of Primes whose digits are composite; primes having only {4, 6, 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 viewerA051416 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L38,188 · 38.19 %
Weight class, k ≤ L61,803 · 61.81 %
Ties, k = L0
On the level line L = 16,922
Forced level, l ≤ d²1,953
Range of a(n)89 … 86,469,446,489
Range of the jump d10 … 34,444,447,800
Largest weight k, level L86,468,995,309, 7,858,969,989

2,348 different gaps occur, from 10 to 34,444,447,800; the level share is 38.19 %; 2.0 % of terms are forced level (l <= d^2); there are no ties; 9 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.