decompwlj 3D

Primes of the form 250n + 1

A179231 on the OEIS · family primes

Weight–level plate of Primes of the form 250n + 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 viewerA179231 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L59,357 · 59.36 %
Weight class, k ≤ L40,641 · 40.64 %
Ties, k = L7
On the level line L = 18,198
Forced level, l ≤ d²2,971
Range of a(n)251 … 179,344,001
Range of the jump d250 … 16,500
Largest weight k, level L179,324,501, 686,751

61 different gaps occur, from 250 to 16,500; the level share is 59.36 %; 3.0 % 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.