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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 A262881 A336820

Adjacent sequences:  A298483 A298484 A298485 * A298487 A298488 A298489

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, Jan 20 2018

STATUS

approved

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Last modified December 5 18:48 EST 2021. Contains 349557 sequences. (Running on oeis4.)