decompwlj 3D

Lesser of twin primes p1 and p2 such that 2*p1+p2 is a prime number

A174913 on the OEIS · family primes

Weight–level plate of Lesser of twin primes p1 and p2 such that 2*p1+p2 is 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 viewerA174913 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,993
Level class, k > L64,073 · 64.08 %
Weight class, k ≤ L35,920 · 35.92 %
Ties, k = L0
On the level line L = 115,240
Forced level, l ≤ d²4,138
Range of a(n)3 … 219,287,669
Range of the jump d2 … 30,870
Largest weight k, level L219,284,327, 12,795,745

1,469 different gaps occur, from 2 to 30,870; the level share is 64.08 %; 4.1 % 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.