decompwlj 3D

Primes of the form 128*k + 1

A208177 on the OEIS · family primes

Weight–level plate of Primes of the form 128*k + 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 viewerA208177 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L52,807 · 52.81 %
Weight class, k ≤ L47,191 · 47.19 %
Ties, k = L11
On the level line L = 15,811
Forced level, l ≤ d²1,842
Range of a(n)257 … 111,679,489
Range of the jump d128 … 10,240
Largest weight k, level L111,670,913, 862,337

73 different gaps occur, from 128 to 10,240; the level share is 52.81 %; 1.8 % of terms are forced level (l <= d^2).

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.