A317387 Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the least positive multiple of n that contains k as a substring in its decimal representation.

1, 10, 2, 12, 2, 3, 12, 12, 30, 4, 10, 12, 3, 4, 5, 12, 20, 32, 24, 50, 6, 14, 12, 30, 4, 15, 6, 7, 16, 21, 30, 40, 52, 6, 70, 8, 18, 24, 35, 24, 5, 16, 27, 8, 9, 10, 27, 32, 14, 54, 60, 72, 18, 90, 10, 11, 20, 36, 24, 35, 6, 70, 8, 9, 10, 11, 12, 22, 30, 45

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Formula

T(n, k) = n * A317175(n, k).

T(1, k) = k.

T(n, n) = n.

T(n, 1) = A317180(n).

Example

Array T(n, k) begins:
  n\k|    1    2    3    4    5    6    7    8    9   10   11   12
  ---+------------------------------------------------------------
    1|    1    2    3    4    5    6    7    8    9   10   11   12
    2|   10    2   30    4   50    6   70    8   90   10  110   12
    3|   12   12    3   24   15    6   27   18    9  102  111   12
    4|   12   12   32    4   52   16   72    8   92  100  112   12
    5|   10   20   30   40    5   60   70   80   90   10  110  120
    6|   12   12   30   24   54    6   72   18   90  102  114   12
    7|   14   21   35   14   35   56    7   28   49  105  112  112
    8|   16   24   32   24   56   16   72    8   96  104  112  112
    9|   18   27   36   45   45   36   27   18    9  108  117  126
   10|   10   20   30   40   50   60   70   80   90   10  110  120

Prog

(PARI) T(n, k, base=10) = { my (w=base^#digits(k, base)); for (m=1, oo, my (mn=m*n); while (mn >= k, if (mn % w == k, return (m*n), mn \= base))) }

Crossrefs

Cf. A317175, A317180.

Sequence in context: A334737 A334837 A327689 * A303784 A278649 A084455

Adjacent sequences: A317384 A317385 A317386 * A317388 A317389 A317390

Keyword

nonn,tabl,base

Author

Rémy Sigrist, Jul 27 2018

Status

approved