decompwlj 3D

Numbers k such that k^2 + 11 is prime

A114274 on the OEIS · family prime values

Weight–level plate of Numbers k such that k^2 + 11 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 viewerA114274 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L23,330 · 23.33 %
Weight class, k ≤ L76,666 · 76.67 %
Ties, k = L1
On the level line L = 10
Forced level, l ≤ d²67
Range of a(n)0 … 5,662,086
Range of the jump d6 … 630
Largest weight k, level L943,499, 808,632

86 different gaps occur, from 6 to 630; the level share is 23.33 %; L = 6 holds 38 % 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.