decompwlj 3D

Primes having only {1, 4, 7} as digits

A079651 on the OEIS · family primes

Weight–level plate of Primes having only {1, 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 viewerA079651 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,984
Level class, k > L33,448 · 33.45 %
Weight class, k ≤ L66,536 · 66.55 %
Ties, k = L0
On the level line L = 19,436
Forced level, l ≤ d²2,062
Range of a(n)7 … 4,444,171,174,747
Range of the jump d4 … 2,333,333,334,600
Largest weight k, level L4,444,171,144,243, 634,881,592,015

790 different gaps occur, from 4 to 2,333,333,334,600; the level share is 33.45 %; 2.1 % of terms are forced level (l <= d^2); there are no ties; 16 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.