decompwlj 3D

Numbers n such that n^2 - 2n + 5 is prime

A089747 on the OEIS · family prime values

Weight–level plate of Numbers n such that n^2 - 2n + 5 is prime
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 viewerA089747 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L21,595 · 21.60 %
Weight class, k ≤ L78,400 · 78.40 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²17
Range of a(n)0 … 1,952,064
Range of the jump d2 … 178
Largest weight k, level L975,739, 650,288

82 different gaps occur, from 2 to 178; the level share is 21.60 %; L = 2 holds 37 % of the level class; 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.