A317387 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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