A248813 A(n,k) is the base-k complement of n; square array A(n,k), n>=0, k>=2, read by antidiagonals.

0, 0, 1, 0, 2, 2, 0, 3, 1, 3, 0, 4, 2, 6, 4, 0, 5, 3, 1, 8, 5, 0, 6, 4, 2, 12, 7, 6, 0, 7, 5, 3, 1, 15, 3, 7, 0, 8, 6, 4, 2, 20, 14, 5, 8, 0, 9, 7, 5, 3, 1, 24, 13, 4, 9, 0, 10, 8, 6, 4, 2, 30, 23, 8, 18, 10, 0, 11, 9, 7, 5, 3, 1, 35, 22, 11, 20, 11, 0, 12, 10, 8, 6, 4, 2, 42, 34, 21, 10, 19, 12

Offset: 0

Author

Alois P. Heinz, Mar 03 2015

Keywords

• nonn
• tabl
• base
• look

Comments

Every column is a permutation of the nonnegative integers.

Examples

			Square array A(n,k) begins:
   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...
   1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, ...
   2,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, ...
   3,  6,  1,  2,  3,  4,  5,  6,  7,  8,  9, ...
   4,  8, 12,  1,  2,  3,  4,  5,  6,  7,  8, ...
   5,  7, 15, 20,  1,  2,  3,  4,  5,  6,  7, ...
   6,  3, 14, 24, 30,  1,  2,  3,  4,  5,  6, ...
   7,  5, 13, 23, 35, 42,  1,  2,  3,  4,  5, ...
   8,  4,  8, 22, 34, 48, 56,  1,  2,  3,  4, ...
   9, 18, 11, 21, 33, 47, 63, 72,  1,  2,  3, ...
  10, 20, 10, 15, 32, 46, 62, 80, 90,  1,  2, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 0..140, flattened
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Columns k=2-16 give: A001477, A004488, A048647, A055115, A055116, A055117, A055118, A055119, A055120, A055121, A055122, A055123, A055124, A055125, A055126.

Programs

Maple

A:= proc(n, k) local t, r, i; t, r:= n, 0;
      for i from 0 while t>0 do
        r:= r+k^i *irem(k-irem(t, k, 't'), k)
      od; r
    end:
seq(seq(A(n, 2+d-n), n=0..d), d=0..14);

PARI

A(n,k)=fromdigits(apply(d->(k-d)%k, digits(n, k)), k); \\ Gheorghe Coserea, Apr 23 2018