decompwlj 3D

Primes congruent to 51 mod 55

A142637 on the OEIS · family primes

Weight–level plate of Primes congruent to 51 mod 55
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 viewerA142637 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L54,649 · 54.65 %
Weight class, k ≤ L45,350 · 45.35 %
Ties, k = L0
On the level line L = 19,511
Forced level, l ≤ d²1,000
Range of a(n)271 … 67,862,021
Range of the jump d110 … 5,940
Largest weight k, level L67,861,361, 609,011

51 different gaps occur, from 110 to 5,940; the level share is 54.65 %; 1.0 % 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.