decompwlj 3D

Numbers k such that k^2 + (k+1)^2 + (k+2)^2 + (k+3)^2 + (k+4)^2 + (k+5)^2 is prime

A027866 on the OEIS · family prime values

Weight–level plate of Numbers k such that k^2 + (k+1)^2 + (k+2)^2 + (k+3)^2 + (k+4)^2 + (k+5)^2 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 viewerA027866 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L21,365 · 21.37 %
Weight class, k ≤ L78,633 · 78.63 %
Ties, k = L17
On the level line L = 17,197
Forced level, l ≤ d²10
Range of a(n)2 … 1,143,041
Range of the jump d1 … 121
Largest weight k, level L1,142,923, 571,520

102 different gaps occur, from 1 to 121; the level share is 21.37 %; L = 1 holds 34 % of the level class.

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.