A004288 Least positive multiple of n written in base 8 using only 0 and 1.

1, 10, 11, 10, 101, 110, 1111111, 10, 11, 1010, 10111, 110, 101, 11111110, 1111, 100, 10001, 110, 1001, 1010, 101011111, 101110, 101001, 110, 1011111, 1010, 1001, 11111110, 1010011, 11110, 11111, 100, 100001, 100010, 100111111, 110

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Programs

Maple

f:= proc(n) local R, S, m, p, Snew, s;
   R[1]:= 1; R[0]:= 0; S:= {0,1};
   for m from 1 do
      p:= 8^m mod n;
      Snew:= map(s -> s + p mod n, S);
      if member(0,Snew) then return R[-p mod n]+10^m fi;
      for s in Snew minus S do R[s] := R[s - p mod n] + 10^m od;
      S:= S union Snew;
    od
end proc:
1, seq(f(n), n=2..100); # Robert Israel, Dec 30 2014

Python

def A004288(n):
    if n > 0:
        for i in range(1, 2**n):
            s = bin(i)[2:]
            if not int(s,8) % n:
                return int(s)
    return 0 # Chai Wah Wu, Dec 30 2014

Extensions

a(11), a(22), a(25) corrected by Chai Wah Wu, Dec 30 2014

Initial 0 deleted and offset corrected by N. J. A. Sloane, Jan 31 2024