login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004290 Least positive multiple of n that when written in base 10 uses only 0's and 1's. 45
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 (list; graph; refs; listen; history; text; internal format)
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.
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
Sequence in context: A282653 A282801 A228006 * A257344 A244859 A159551
KEYWORD
nonn,base,nice
AUTHOR
EXTENSIONS
Initial 0 deleted and offset corrected by N. J. A. Sloane, Jan 31 2024
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)