decompwlj 3D

Symmetric primes: an odd prime p is symmetric if there exists an odd prime q such that |p-q| = gcd(p-1,q-1)

A090190 on the OEIS · family primes

Weight–level plate of Symmetric primes: an odd prime p is symmetric if there exists an odd prime q such that |p-q| = gcd(p-1,q-1)
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 viewerA090190 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L23,823 · 23.82 %
Weight class, k ≤ L76,174 · 76.18 %
Ties, k = L20
On the level line L = 17,332
Forced level, l ≤ d²9
Range of a(n)3 … 1,586,719
Range of the jump d2 … 192
Largest weight k, level L1,586,527, 528,873

75 different gaps occur, from 2 to 192; the level share is 23.82 %; L = 1 holds 31 % 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.