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A334620 a(n) is the smallest multiple of n formed by the concatenation 1,2,3,...,k for some k.

%I A334620 #43 Apr 04 2022 08:56:48
%S A334620 1,12,12,12,12345,12,1234567891011,123456,12345678,12345678910,
%T A334620 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106,
%U A334620 12
%N A334620 a(n) is the smallest multiple of n formed by the concatenation 1,2,3,...,k for some k.
%H A334620 Robert Israel, <a href="/A334620/b334620.txt">Table of n, a(n) for n = 1..144</a>
%F A334620 a(n) is the smallest multiple of n appearing in A007908.
%e A334620 a(3) = 12, because 12 is the smallest multiple of 3 that appears in A007908.
%p A334620 f:= proc(n) local x,i;
%p A334620 x:= 0;
%p A334620 for i from 1 do
%p A334620   x:= x*10^(1+ilog10(i))+i;
%p A334620   if x mod n = 0 then return x fi
%p A334620 od
%p A334620 end proc:
%p A334620 map(f, [$1..20]); # _Robert Israel_, Oct 25 2020
%t A334620 smn[n_]:=Module[{k=1,c=1},While[!Divisible[c,n],k++;c= c*10^IntegerLength[ k]+ k];c]; Array[ smn,20] (* _Harvey P. Dale_, Apr 04 2022 *)
%o A334620 (PARI) a(n) = j="";for(k=1, oo, j=eval(concat(Str(j), k)); if(j%n==0, return(j)))
%Y A334620 Cf. A007908, A075002.
%K A334620 nonn,base,easy
%O A334620 1,2
%A A334620 _Eder Vanzei_, Sep 09 2020