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

0,6

Comments

The corresponding sequence for the binary base is A295653.

Links

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

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).

Example

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  ...

Prog

(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

Crossrefs

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

Sequence in context: A025682 A025691 A002262 * A189768 A362327 A350168

Adjacent sequences: A298483 A298484 A298485 * A298487 A298488 A298489

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Jan 20 2018

Status

approved