decompwlj 3D

Primes congruent to 21 mod 47

A142372 on the OEIS · family primes

Weight–level plate of Primes congruent to 21 mod 47
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 viewerA142372 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L51,116 · 51.12 %
Weight class, k ≤ L48,882 · 48.88 %
Ties, k = L7
On the level line L = 16,253
Forced level, l ≤ d²1,251
Range of a(n)397 … 78,826,541
Range of the jump d94 … 7,050
Largest weight k, level L78,818,081, 826,845

71 different gaps occur, from 94 to 7,050; the level share is 51.12 %; 1.3 % of terms are forced level (l <= d^2).

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.