decompwlj 3D

Primes p for which the period of 1/p is prime

A072859 on the OEIS · family primes

Weight–level plate of Primes p for which the period of 1/p 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 viewerA072859 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L47,804 · 47.80 %
Weight class, k ≤ L52,194 · 52.20 %
Ties, k = L0
On the level line L = 110,591
Forced level, l ≤ d²522
Range of a(n)11 … 38,376,587
Range of the jump d2 … 4,516
Largest weight k, level L38,375,507, 12,720,585

1,150 different gaps occur, from 2 to 4,516; the level share is 47.80 %; 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.