decompwlj 3D

Numbers with the property that every pair of adjacent digits sum to a prime number

A182175 on the OEIS · family digit rule

Weight–level plate of Numbers with the property that every pair of adjacent digits sum to a prime number
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 viewerA182175 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L14,514 · 14.51 %
Weight class, k ≤ L85,483 · 85.49 %
Ties, k = L7
On the level line L = 16,646
Forced level, l ≤ d²733
Range of a(n)0 … 58,385,076
Range of the jump d1 … 3,434,344
Largest weight k, level L58,383,019, 29,192,514

87 different gaps occur, from 1 to 3,434,344; the level share is 14.51 %; L = 1 holds 46 % of the level class.

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.