decompwlj 3D

Primes p such that p^2-p-1 is prime

A091567 on the OEIS · family primes

Weight–level plate of Primes p such that p^2-p-1 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 viewerA091567 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L40,351 · 40.35 %
Weight class, k ≤ L59,644 · 59.65 %
Ties, k = L4
On the level line L = 18,194
Forced level, l ≤ d²152
Range of a(n)3 … 14,807,981
Range of the jump d2 … 1,542
Largest weight k, level L14,807,873, 4,921,415

561 different gaps occur, from 2 to 1,542; the level share is 40.35 %.

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.