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A076924
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Smallest multiple of the n-th prime not containing any of its digits, or 0 if no such number exists.
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2
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4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 111, 82, 86, 188, 106, 118, 244, 134, 284, 146, 158, 166, 267, 388, 2222, 824, 428, 327, 226, 508, 262, 548, 278, 2086, 302, 628, 489, 334, 692, 358, 362, 382, 772, 2364, 2388, 633, 446, 454, 458, 466, 478, 3856, 4769
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OFFSET
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1,1
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COMMENTS
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a(n) = 0 if and only if prime(n) contains all decimal digits with the possible exception of 0. Otherwise, if n > 3 and p=prime(n) does not contain the nonzero digit k, the repdigit (10^m-1)*k/9 is a multiple of p where m is the order of 10 mod p. - Robert Israel, Jul 21 2020
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LINKS
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FORMULA
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MAPLE
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f:= proc(n) local p, k, r, D;
D:= convert(convert(n, base, 10), set);
for k from 2 to 10^(1+ilog10(n)) do
r:= k*n;
if convert(convert(r, base, 10), set) intersect D = {} then return r fi
od;
error ("search failed for n=%1", n)
end proc:
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MATHEMATICA
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smp[p_]:=Module[{k=2}, While[ContainsAny[IntegerDigits[k*p], IntegerDigits[ p]], k++]; k*p]; Table[smp[p], {p, Prime[Range[60]]}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 19 2019 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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