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A004290 Least positive multiple of n that when written in base 10 uses only 0's and 1's. 35
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, Table of n, a(n) for n = 0..1999 (from 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

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-Fran├žois 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

CROSSREFS

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

Sequence in context: A119484 A100751 A228006 * A244859 A159551 A105991

Adjacent sequences:  A004287 A004288 A004289 * A004291 A004292 A004293

KEYWORD

nonn,base,nice

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 24 16:46 EST 2014. Contains 249899 sequences.