decompwlj 3D

Primes having only {0, 1, 4} as digits

A260266 on the OEIS · family primes

Weight–level plate of Primes having only {0, 1, 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 viewerA260266 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,976
Level class, k > L39,441 · 39.45 %
Weight class, k ≤ L60,535 · 60.55 %
Ties, k = L0
On the level line L = 16,299
Forced level, l ≤ d²2,865
Range of a(n)11 … 40,141,144,444,001
Range of the jump d10 … 25,555,555,555,600
Largest weight k, level L40,141,144,107,781, 3,649,181,819,181

4,199 different gaps occur, from 10 to 25,555,555,555,600; the level share is 39.45 %; 2.9 % 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.