A004290 Least positive multiple of n that when written in base 10 uses only 0's and 1's.

1, 10, 111, 100, 10, 1110, 1001, 1000, 111111111, 10, 11, 11100, 1001, 10010, 1110, 10000, 11101, 1111111110, 11001, 100, 10101, 110, 110101, 111000, 100, 10010, 1101111111, 100100, 1101101, 1110, 111011, 100000, 111111, 111010

Offset

1,2

Comments

It is easy to show that a(n) always exists and in fact has at most n digits [Wu, 2014]. - N. J. A. Sloane, Jun 13 2014

a(n) = min{A007088(k): k > 0 and A007088(k) mod n = 0}. - Reinhard Zumkeller, Jan 10 2012

Links

Chai Wah Wu, Table of n, a(n) for n = 0..9998 (first 2000 terms from T. D. Noe [and Ed Pegg Link])

Ed Pegg Jr., 'Binary' Puzzle.

Eric M. Schmidt, Sage code to compute this sequence.

Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Formula

a(n) = n*A079339(n). - Jonathan Sondow, Jun 15 2014

Maple

f:= proc(n)
local L, x, m, r, k, j;
for x from 2 to n-1 do L[0, x]:= 0 od:
L[0, 0]:= 1: L[0, 1]:= 1;
for m from 1 do
   if L[m-1, (-10^m) mod n] = 1 then break fi;
   L[m, 0]:= 1;
   for k from 1 to n-1 do
     L[m, k]:= max(L[m-1, k], L[m-1, k-10^m mod n])
   od;
od;
r:= 10^m; k:= -10^m mod n;
for j from m-1 by -1 to 1 do
    if L[j-1, k] = 0 then
      r:= r + 10^j; k:= k - 10^j mod n;
    fi
od;
if k = 1 then r:= r + 1 fi;
r
end proc:
0, 1, seq(f(n), n=2..100); # Robert Israel, Feb 09 2016

Mathematica

a[n_] := For[k = 1, True, k++, b = FromDigits[ IntegerDigits[k, 2] ]; If[Mod[b, n] == 0, Return[b]]]; a[0] = 0; Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Jun 14 2013, after Reinhard Zumkeller *)
With[{c=Rest[Union[FromDigits/@Flatten[Table[Tuples[{1, 0}, i], {i, 10}], 1]]]}, Join[{0}, Flatten[ Table[ Select[c, Divisible[#, n]&, 1], {n, 40}]]]] (* Harvey P. Dale, Dec 07 2013 *)

Prog

(Haskell)
a004290 0 = 0
a004290 n = head [x | x <- tail a007088_list, mod x n == 0]
-- Reinhard Zumkeller, Jan 10 2012
(Python) def A004290(n):
    if n > 0:
        for i in range(1, 2**n):
            x = int(bin(i)[2:])
            if not x % n:
                return x
    return 0
# Chai Wah Wu, Dec 30 2014
(PARI) a(n) = {if( n==0, return (0)); my(m = n); while (vecmax(digits(m)) != 1, m+=n); m; } \\ Michel Marcus, Feb 09 2016, May 27 2020

Crossrefs

Cf. A004283-A004289, A078241-A078248, A079339, A096681-A096688, A257345.

Sequence in context: A282653 A282801 A228006 * A257344 A244859 A159551

Adjacent sequences: A004287 A004288 A004289 * A004291 A004292 A004293

Keyword

nonn,base,nice

Author

David W. Wilson

Extensions

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

Status

approved