A298486 Square array T(n, k), n >= 0, k >= 0, read by antidiagonals upwards: T(n, k) = the (k+1)-th nonnegative number m such that n + m can be computed with carry in decimal base.

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 1, 20, 11, 11, 11, 11, 11, 11, 11, 11, 11, 0, 1

Offset: 0

Author

Rémy Sigrist, Jan 20 2018

Keywords

• nonn
• base
• tabl

Comments

The corresponding sequence for the binary base is A295653.

Examples

			Square array begins:
  n\k|  0   1   2   3   4   5   6   7   8   9   10  ...
  ---+-------------------------------------------------
    0|  0   1   2   3   4   5   6   7   8   9   10  ... <-- A001477
    1|  0   1   2   3   4   5   6   7   8  10   11  ...
    2|  0   1   2   3   4   5   6   7  10  11   12  ...
    3|  0   1   2   3   4   5   6  10  11  12   13  ...
    4|  0   1   2   3   4   5  10  11  12  13   14  ...
    5|  0   1   2   3   4  10  11  12  13  14   20  ...
    6|  0   1   2   3  10  11  12  13  20  21   22  ...
    7|  0   1   2  10  11  12  20  21  22  30   31  ...
    8|  0   1  10  11  20  21  30  31  40  41   50  ...
    9|  0  10  20  30  40  50  60  70  80  90  100  ... <-- A008592
   10|  0   1   2   3   4   5   6   7   8   9   10  ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..5150

Crossrefs

Cf. A001477, A004218, A008592, A122840, A295653, A298372.

Programs

PARI

T(n,k,{base=10}) = my (v=0, p=1); while (k, my (r=base - (n%base)); v += p*(k%r); n \= base; k \= r; p *= base); v

Formula

For any n >= 0 and k >= 0:

- T(0, k) = k,

- T(9, k) = 10 * k,

- T(10^n - 1, k) = 10^n * k,

- T(n, 0) = 0,

- T(n, 1) = 10^A122840(n+1),

- T(n, k + A298372(n)) = k + 10^A004218(n+1) (i.e. each row is linear).