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

0,4

Comments

The nonnegative integers together with A form an abelian group; A354469 gives inverse elements.

Each row is a permutation of the nonnegative integers.

Links

Table of n, a(n) for n=0..77.

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

Formula

A(n, k) = A(k, n).

A(m, A(n, k)) = A(A(m, n), k).

A(n, 0) = n.

A(n, k) = 0 iff k = A354469(n).

A(n, 1) = A004442(n).

Example

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

Prog

(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)) }

Crossrefs

Cf. A004442, A235168, A354438 (factorial base analog), A354469.

Sequence in context: A307301 A307300 A354438 * A141692 A261097 A335335

Adjacent sequences: A354467 A354468 A354469 * A354471 A354472 A354473

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Jun 02 2022

Status

approved