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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.
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%I #5 Jul 28 2018 11:13:58

%S 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,

%T 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,

%U 72,18,90,10,11,20,36,24,35,6,70,8,9,10,11,12,22,30,45

%N 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.

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

%F T(1, k) = k.

%F T(n, n) = n.

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

%e Array T(n, k) begins:

%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12

%e ---+------------------------------------------------------------

%e 1| 1 2 3 4 5 6 7 8 9 10 11 12

%e 2| 10 2 30 4 50 6 70 8 90 10 110 12

%e 3| 12 12 3 24 15 6 27 18 9 102 111 12

%e 4| 12 12 32 4 52 16 72 8 92 100 112 12

%e 5| 10 20 30 40 5 60 70 80 90 10 110 120

%e 6| 12 12 30 24 54 6 72 18 90 102 114 12

%e 7| 14 21 35 14 35 56 7 28 49 105 112 112

%e 8| 16 24 32 24 56 16 72 8 96 104 112 112

%e 9| 18 27 36 45 45 36 27 18 9 108 117 126

%e 10| 10 20 30 40 50 60 70 80 90 10 110 120

%o (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))) }

%Y Cf. A317175, A317180.

%K nonn,tabl,base

%O 1,2

%A _Rémy Sigrist_, Jul 27 2018