A244954 Smallest positive multiple of n whose base-3 representation contains only 0's and 1's.
1, 4, 3, 4, 10, 12, 28, 40, 9, 10, 121, 12, 13, 28, 30, 112, 85, 36, 247, 40, 84, 352, 253, 120, 325, 364, 27, 28, 841, 30, 31, 256, 363, 850, 280, 36, 37, 760, 39, 40, 82, 84, 3010, 352, 90, 1012, 94, 336, 2548, 850, 255, 364, 742, 108, 2200, 112, 741
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Ed Pegg Jr., 'Binary' Puzzle
- Eric M. Schmidt, Sage code to compute this sequence (use b=3)
- Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.
Programs
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Mathematica
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 *) -
PARI
a(n,b=3) = if (n, k=1; while(vecmax(digits(k*n, b))>1, k++); k*n); \\ Michel Marcus, Jul 10 2014
Extensions
Data changed, offset changed, Mathematica program replaced, and b-file replaced by Harvey P. Dale, Feb 01 2024