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Smallest positive multiple of n whose base-3 representation contains only 0's and 1's.
7

%I #23 Feb 01 2024 15:46:07

%S 1,4,3,4,10,12,28,40,9,10,121,12,13,28,30,112,85,36,247,40,84,352,253,

%T 120,325,364,27,28,841,30,31,256,363,850,280,36,37,760,39,40,82,84,

%U 3010,352,90,1012,94,336,2548,850,255,364,742,108,2200,112,741

%N Smallest positive multiple of n whose base-3 representation contains only 0's and 1's.

%H Harvey P. Dale, <a href="/A244954/b244954.txt">Table of n, a(n) for n = 1..1000</a>

%H Ed Pegg Jr., <a href="http://www.mathpuzzle.com/Binary.html">'Binary' Puzzle</a>

%H Eric M. Schmidt, <a href="/A004290/a004290_1.sage.txt">Sage code to compute this sequence</a> (use b=3)

%H Chai Wah Wu, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.121.06.529">Pigeonholes and repunits</a>, Amer. Math. Monthly, 121 (2014), 529-533.

%t Module[{nn=10,b3},b3=Rest[FromDigits[#,3]&/@Tuples[{0,1},nn]];Table[SelectFirst[b3,Mod[ #,n]==0&],{n,60}]] (* _Harvey P. Dale_, Feb 01 2024 *)

%o (PARI) a(n,b=3) = if (n, k=1; while(vecmax(digits(k*n, b))>1, k++); k*n); \\ _Michel Marcus_, Jul 10 2014

%Y Cf. A004283 (written in base 3), A004290, A244955-A244960.

%K nonn,base

%O 1,2

%A _Eric M. Schmidt_, Jul 09 2014

%E Data changed, offset changed, Mathematica program replaced, and b-file replaced by _Harvey P. Dale_, Feb 01 2024