A273315 and a316572 and Wilson theorem

[Davide Rotondo]

Hi to all, dearest fans what do you think about this...

i noticed that A273315 and a316572 are correlated each other with a method inspired by Wilson theorem that I show down below...

METHOD FOR OBTAINING https://oeis.org/A273315 : “First differences (i.e., the differences between successive terms) of the number of active (lit, black) cells in the nth growth stage of a two-dimensional cellular automaton defined by the ‘643 Rule’, based on the 5-cell von Neumann neighborhood.”
DATA
4, 12, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432

METHOD

Consider the minimum k greater than a(k-1) such that (n-1)!+k is divisible by n.

EXAMPLES
n. k
1. 1
2. 4
3. 6
4. 11
5. 12
...

CONSIDERATION

Note that for odd n and starting from n=3, k*2 gives the above sequence.

n.b.
https://oeis.org/A316571

See you soon

Davide