decompwlj 3D

Primes of the form 33164857769 + 2*n^2

A271818 on the OEIS · family primes

Weight–level plate of Primes of the form 33164857769 + 2*n^2
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 viewerA271818 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L98,379 · 98.38 %
Weight class, k ≤ L1,621 · 1.62 %
Ties, k = L0
On the level line L = 16,368
Forced level, l ≤ d²93,355
Range of a(n)33,164,857,769 … 300,311,732,827
Range of the jump d2 … 42,992,384
Largest weight k, level L300,304,423,333, 11,054,952,589

98,683 different gaps occur, from 2 to 42,992,384; the level share is 98.38 %; 93.4 % 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.