decompwlj 3D

Primes having only {0, 1, 3} as digits

A260044 on the OEIS · family primes

Weight–level plate of Primes having only {0, 1, 3} 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 viewerA260044 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,975
Level class, k > L30,288 · 30.30 %
Weight class, k ≤ L69,687 · 69.70 %
Ties, k = L1
On the level line L = 14,229
Forced level, l ≤ d²1,822
Range of a(n)3 … 10,001,130,010,303
Range of the jump d2 … 6,666,666,667,012
Largest weight k, level L10,001,113,129,951, 3,333,710,000,333

3,491 different gaps occur, from 2 to 6,666,666,667,012; the level share is 30.30 %; 1.8 % of terms are forced level (l <= d^2); 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.