decompwlj 3D

Primes of the form 24x^2+35y^2

A139994 on the OEIS · family quadratic form

Weight–level plate of Primes of the form 24x^2+35y^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 viewerA139994 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L54,956 · 54.96 %
Weight class, k ≤ L45,040 · 45.04 %
Ties, k = L0
On the level line L = 116,804
Forced level, l ≤ d²806
Range of a(n)59 … 53,563,739
Range of the jump d48 … 5,040
Largest weight k, level L53,559,563, 1,092,947

108 different gaps occur, from 48 to 5,040; the level share is 54.96 %; L = 1 holds 31 % 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.