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 A004290 Least positive multiple of n that when written in base 10 uses only 0's and 1's. 44
 0, 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 0,3 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 T. D. Noe and 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) for n > 0. - 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 STATUS approved

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Last modified October 20 12:27 EDT 2020. Contains 337904 sequences. (Running on oeis4.)