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Triangle read by rows: The number of digits in the smallest 9-repdigit that is a multiple of n and m, where n and m are coprime to 2 and 5.
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%I #11 Feb 08 2023 07:23:31

%S 1,1,1,6,6,42,1,3,6,9,2,2,6,2,22,6,6,6,6,6,78,16,16,48,16,16,48,272,

%T 18,18,18,18,18,18,144,342,6,6,42,6,6,6,48,18,42,22,22,66,22,22,66,

%U 176,198,66,506,3,9,6,27,6,6,48,18,18,66,81,28,28,84,28,28,84,112,252,84,308,84,812

%N Triangle read by rows: The number of digits in the smallest 9-repdigit that is a multiple of n and m, where n and m are coprime to 2 and 5.

%C The number of digits of the smallest member of A002283 divisible by n and m, as n and m run through A045572. Numbers of the form 10^d-1 are not divisible through 5 or 2, so these are excluded in the table. Losely related to A278588.

%F T(i,j) = min{d: (n*m) | (10^d-1)} where n=A045572(i) and m=A045572(j).

%e The 3rd smallest number coprime to 2 and 5 is A045572(3)=7. The smallest 9-repdigit divisible by 7*7=49 is 10^42-1 = A002283(42), to T(3,3)=42.

%e The triangle starts

%e 1;

%e 1, 1;

%e 6, 6, 42;

%e 1, 3, 6, 9;

%e 2, 2, 6, 2, 22;

%e 6, 6, 6, 6, 6, 78;

%e 16, 16, 48, 16, 16, 48, 272;

%Y Cf. A002283, A002329, A045572

%K nonn,tabl,base

%O 1,4

%A _R. J. Mathar_, Dec 14 2016