decompwlj 3D

Lesser members of twin prime pairs of form (4*k+3, 4*k+5), k >= 0

A071698 on the OEIS · family primes

Weight–level plate of Lesser members of twin prime pairs of form (4*k+3, 4*k+5), 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 viewerA071698 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L52,306 · 52.31 %
Weight class, k ≤ L47,690 · 47.69 %
Ties, k = L0
On the level line L = 116,110
Forced level, l ≤ d²542
Range of a(n)3 … 40,820,291
Range of the jump d8 … 4,284
Largest weight k, level L40,817,759, 2,368,651

279 different gaps occur, from 8 to 4,284; the level share is 52.31 %; L = 1 holds 31 % 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.