A354470 Square array A(n, k), n, k >= 0, read by antidiagonals; the primorial base expansion of A(n, k) is obtained by adding componentwise and reducing modulo their radix the digits of the primorial 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 24 25 26 27
13| 13 12 15 14 17 16 19 18 21 20 23 22 25 24 27 26
14| 14 15 16 17 12 13 20 21 22 23 18 19 26 27 28 29
15| 15 14 17 16 13 12 21 20 23 22 19 18 27 26 29 28
Links
- Rémy Sigrist, Colored representation of the array A(n, k) for n, k < 2*3*5*7*11 (the hue is function of A(n, k), black pixels correspond to 0's)
- Index entries for sequences related to primorial base
Programs
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PARI
A(n,k, s=i->prime(i)) = { 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