decompwlj 3D

Greater members of twin prime pairs of form (4*k+1,4*k+3), k>0

A071696 on the OEIS · family primes

Weight–level plate of Greater members of twin prime pairs of form (4*k+1,4*k+3), k>0
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 viewerA071696 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L51,732 · 51.73 %
Weight class, k ≤ L48,264 · 48.27 %
Ties, k = L0
On the level line L = 116,456
Forced level, l ≤ d²531
Range of a(n)7 … 40,692,523
Range of the jump d12 … 5,088
Largest weight k, level L40,688,779, 3,128,239

282 different gaps occur, from 12 to 5,088; the level share is 51.73 %; L = 1 holds 32 % of the level class; there are no ties.

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.