A112889 a(n) is the least nonnegative integer in base 10 containing n zeros that is divisible by n.

0, 100, 3000, 10000, 100000, 3000000, 70000000, 100000000, 9000000000, 10000000000, 1000000000010, 3000000000000, 100000000000004, 700000000000000, 3000000000000000, 10000000000000000, 1000000000000000002, 9000000000000000000, 100000000000000000090

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..993

Formula

a(n) = n*A112890(n).

Example

a(3) = 3000 because 3000 contains 3 zeros and is divisible by 3.

Maple

f:= proc(n) local d, x, y, z, d2, v;
     for x from 1 to 9 do if x*10^n mod n = 0 then return x*10^n fi od;
     for y from 1 to 9 do
       for d from 0 to n do
         for x from 1 to 9 do
           v:= y*10^(n+1) + x*10^d;
           if v mod n = 0 then return v fi;
    od od od;
    for z from 1 to 9 do
      for d from 2 to n+1 do
        for y from 1 to 9 do
          for d2 from 0 to d-1 do
            for x from 1 to 9 do
              v:= z*10^(n+2) + y*10^d + x*10^d2;
              if v mod n = 0 then return v fi;
    od od od od od;
    FAIL
end proc:
f(1):= 0:
map(f, [$1..50]); # Robert Israel, Jul 10 2023

Crossrefs

Cf. A112890-A112898, A112900-A112905, A112907-A112910.

Sequence in context: A075822 A250845 A200937 * A118490 A146310 A117685

Adjacent sequences: A112886 A112887 A112888 * A112890 A112891 A112892

Keyword

base,nonn

Author

Ray G. Opao, Oct 05 2005

Extensions

Extended by Ray Chandler, Oct 09 2005

Status

approved