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A337241
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a(n) is the least k such that the decimal representation of k*n contains at least two digits which are the same.
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3
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11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 1, 12, 9, 8, 15, 7, 7, 8, 6, 5, 12, 1, 5, 6, 4, 13, 37, 4, 4, 10, 5, 7, 1, 8, 13, 4, 3, 3, 3, 5, 13, 6, 8, 1, 5, 7, 3, 3, 7, 2, 5, 13, 4, 20, 1, 2, 2, 2, 2, 5, 2, 7, 4, 7, 7, 1, 5, 4, 6, 10, 5, 2, 4, 3, 3, 3, 1, 11, 6, 5, 14, 8, 2, 3, 3
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OFFSET
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1,1
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COMMENTS
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First differs from A045538 at a(21) = 12 since 21 * 12 = 252 contains two equal but not consecutive digits. A045538(21) = 16.
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LINKS
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FORMULA
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EXAMPLE
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a(21) = 12 because 21*12 = 252 is the smallest multiple of 21 with equal digits.
a(23) = 5 because 23*5 = 115 is the smallest multiple of 23 with equal digits.
a(34) = 8 because 34*8 = 272 is the smallest multiple of 34 with equal digits.
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MAPLE
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f:= proc(n) local k, L;
for k from 1 do
L:= convert(k*n, base, 10);
if nops(convert(L, set))<nops(L) then return k fi
od;
end proc:
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MATHEMATICA
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a[n_] := Module[{k = 1}, While[Max@ (Last /@ Tally @ IntegerDigits[k*n]) == 1, k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 22 2020 *)
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PROG
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(PARI) a(n) = {my(k=1, d=digits(n)); while(#Set(d) == #d, k++; d=digits(k*n)); k; } \\ Michel Marcus, Aug 22 2020
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CROSSREFS
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Cf. A045538 (where the 2 digits must be consecutive), A337240 (resulting k*n).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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