decompwlj 3D

Primes of the form 17*k - 1

A140541 on the OEIS · family primes

Weight–level plate of Primes of the form 17*k - 1
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 viewerA140541 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L44,559 · 44.56 %
Weight class, k ≤ L55,438 · 55.44 %
Ties, k = L12
On the level line L = 16,654
Forced level, l ≤ d²338
Range of a(n)67 … 25,592,071
Range of the jump d34 … 2,992
Largest weight k, level L25,591,459, 729,843

64 different gaps occur, from 34 to 2,992; the level share is 44.56 %.

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.