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

1, 12, 12, 12, 12345, 12, 1234567891011, 123456, 12345678, 12345678910, 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106, 12

Offset: 1

Author

Eder Vanzei, Sep 09 2020

Keywords

• nonn
• base
• easy

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..144

Crossrefs

Cf. A007908, A075002.

Programs

Maple

f:= proc(n) local x,i;
x:= 0;
for i from 1 do
  x:= x*10^(1+ilog10(i))+i;
  if x mod n = 0 then return x fi
od
end proc:
map(f, [$1..20]); # Robert Israel, Oct 25 2020

Mathematica

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 *)

PARI

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

Formula

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