A248813 - OEIS

%I #50 Apr 23 2018 10:18:38

%S 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,

%T 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,

%U 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

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

%C Every column is a permutation of the nonnegative integers.

%H Alois P. Heinz, <a href="/A248813/b248813.txt">Antidiagonals n = 0..140, flattened</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>

%e Square array A(n,k) begins:

%e    0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...

%e    1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, ...

%e    2,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, ...

%e    3,  6,  1,  2,  3,  4,  5,  6,  7,  8,  9, ...

%e    4,  8, 12,  1,  2,  3,  4,  5,  6,  7,  8, ...

%e    5,  7, 15, 20,  1,  2,  3,  4,  5,  6,  7, ...

%e    6,  3, 14, 24, 30,  1,  2,  3,  4,  5,  6, ...

%e    7,  5, 13, 23, 35, 42,  1,  2,  3,  4,  5, ...

%e    8,  4,  8, 22, 34, 48, 56,  1,  2,  3,  4, ...

%e    9, 18, 11, 21, 33, 47, 63, 72,  1,  2,  3, ...

%e   10, 20, 10, 15, 32, 46, 62, 80, 90,  1,  2, ...

%p A:= proc(n, k) local t, r, i; t, r:= n, 0;

%p       for i from 0 while t>0 do

%p         r:= r+k^i *irem(k-irem(t, k, 't'), k)

%p       od; r

%p     end:

%p seq(seq(A(n, 2+d-n), n=0..d), d=0..14);

%o (PARI) A(n,k)=fromdigits(apply(d->(k-d)%k, digits(n, k)), k); \\ _Gheorghe Coserea_, Apr 23 2018

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

%K nonn,tabl,base,look

%O 0,5

%A _Alois P. Heinz_, Mar 03 2015