decompwlj 3D

Primes composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}

A247052 on the OEIS · family primes

Weight–level plate of Primes composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}
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 viewerA247052 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,993
Level class, k > L32,476 · 32.48 %
Weight class, k ≤ L67,517 · 67.52 %
Ties, k = L0
On the level line L = 16,036
Forced level, l ≤ d²1,405
Range of a(n)2 … 544,254,241
Range of the jump d2 … 133,333,400
Largest weight k, level L544,251,403, 77,749,645

1,077 different gaps occur, from 2 to 133,333,400; the level share is 32.48 %; 1.4 % of terms are forced level (l <= d^2); there are no ties; 7 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.