decompwlj 3D

Fouvry-Iwaniec primes: Primes of the form k^2 + p^2 where p is a prime

A185086 on the OEIS · family primes

Weight–level plate of Fouvry-Iwaniec primes: Primes of the form k^2 + p^2 where p is a 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 viewerA185086 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L37,665 · 37.67 %
Weight class, k ≤ L62,333 · 62.33 %
Ties, k = L9
On the level line L = 19,129
Forced level, l ≤ d²67
Range of a(n)5 … 9,423,413
Range of the jump d4 … 1,012
Largest weight k, level L9,422,657, 1,879,797

202 different gaps occur, from 4 to 1,012; the level share is 37.67 %.

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.