decompwlj 3D

Difference between squares of twin prime pairs

A111046 on the OEIS · family primes

Weight–level plate of Difference between squares of twin prime pairs
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 viewerA111046 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L32,329 · 32.33 %
Weight class, k ≤ L67,667 · 67.67 %
Ties, k = L0
On the level line L = 13
Forced level, l ≤ d²1,055
Range of a(n)16 … 73,636,800
Range of the jump d8 … 8,760
Largest weight k, level L3,068,069, 2,714,912

247 different gaps occur, from 8 to 8,760; the level share is 32.33 %; 1.1 % of terms are forced level (l <= d^2); 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.