A354438 Square array A(n, k), n, k >= 0, read by antidiagonals; the factorial base expansion of A(n, k) is obtained by adding componentwise and reducing modulo their radix the digits of the factorial base expansions of n and k.
0, 1, 1, 2, 0, 2, 3, 3, 3, 3, 4, 2, 4, 2, 4, 5, 5, 5, 5, 5, 5, 6, 4, 0, 4, 0, 4, 6, 7, 7, 1, 1, 1, 1, 7, 7, 8, 6, 8, 0, 2, 0, 8, 6, 8, 9, 9, 9, 9, 3, 3, 9, 9, 9, 9, 10, 8, 10, 8, 10, 2, 10, 8, 10, 8, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
Offset: 0
Examples
Square array A(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+----------------------------------------------------------------
0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1| 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14
2| 2 3 4 5 0 1 8 9 10 11 6 7 14 15 16 17
3| 3 2 5 4 1 0 9 8 11 10 7 6 15 14 17 16
4| 4 5 0 1 2 3 10 11 6 7 8 9 16 17 12 13
5| 5 4 1 0 3 2 11 10 7 6 9 8 17 16 13 12
6| 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
7| 7 6 9 8 11 10 13 12 15 14 17 16 19 18 21 20
8| 8 9 10 11 6 7 14 15 16 17 12 13 20 21 22 23
9| 9 8 11 10 7 6 15 14 17 16 13 12 21 20 23 22
10| 10 11 6 7 8 9 16 17 12 13 14 15 22 23 18 19
11| 11 10 7 6 9 8 17 16 13 12 15 14 23 22 19 18
12| 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3
13| 13 12 15 14 17 16 19 18 21 20 23 22 1 0 3 2
14| 14 15 16 17 12 13 20 21 22 23 18 19 2 3 4 5
15| 15 14 17 16 13 12 21 20 23 22 19 18 3 2 5 4
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)
- Rémy Sigrist, Colored representation of the array A(n, k) for n, k < 7! (the hue is function of A(n, k), black pixels correspond to 0's)
- Index entries for sequences related to factorial base representation
Programs
-
PARI
A(n,k, s=i->i+1) = { my (v=0, f=1, r); for (i=1, oo, if (n==0 && k==0, return (v), r=s(i); v+=f*((n+k)%r); f*=r; n\=r; k\=r)) }
Comments