%I #43 Apr 04 2022 08:56:48

%S 1,12,12,12,12345,12,1234567891011,123456,12345678,12345678910,

%T 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106,

%U 12

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

%H Robert Israel, <a href="/A334620/b334620.txt">Table of n, a(n) for n = 1..144</a>

%F a(n) is the smallest multiple of n appearing in A007908.

%e a(3) = 12, because 12 is the smallest multiple of 3 that appears in A007908.

%p f:= proc(n) local x,i;

%p x:= 0;

%p for i from 1 do

%p x:= x*10^(1+ilog10(i))+i;

%p if x mod n = 0 then return x fi

%p od

%p end proc:

%p map(f, [$1..20]); # _Robert Israel_, Oct 25 2020

%t 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 (PARI) a(n) = j="";for(k=1, oo, j=eval(concat(Str(j), k)); if(j%n==0, return(j)))

%Y Cf. A007908, A075002.

%K nonn,base,easy

%O 1,2

%A _Eder Vanzei_, Sep 09 2020