decompwlj 3D

Primes congruent to 1 mod 49

A142414 on the OEIS · family primes

Weight–level plate of Primes congruent to 1 mod 49
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 viewerA142414 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L52,478 · 52.48 %
Weight class, k ≤ L47,518 · 47.52 %
Ties, k = L2
On the level line L = 17,147
Forced level, l ≤ d²1,092
Range of a(n)197 … 71,458,759
Range of the jump d98 … 6,370
Largest weight k, level L71,443,079, 721,477

62 different gaps occur, from 98 to 6,370; the level share is 52.48 %; 1.1 % 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.