A244958 Smallest positive multiple of n whose base-7 representation contains only 0's and 1's.

1, 8, 57, 8, 50, 19608, 7, 8, 351, 50, 2409, 19608, 351, 56, 2745, 400, 16864, 134856, 57, 400, 399, 2794, 17158, 19608, 50, 19552, 351, 56, 137257, 120450, 16864, 2752, 2409, 16864, 350, 134856, 117993, 19608, 351, 400, 134849, 137256, 344, 16808, 2745

Offset: 1

Author

Eric M. Schmidt, Jul 09 2014

Keywords

• nonn
• base

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=7)
• Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Crossrefs

Cf. A004287 (written in base 7), A004290, A244954-A244960.

Programs

Mathematica

With[{cl=Rest[{FromDigits[#,7],FromDigits[#]}&/@Tuples[{0,1},7]]},Table[SelectFirst[cl,Mod[ #[[1]],n]==0&],{n,50}]][[;;,1]] (* Harvey P. Dale, Feb 01 2024 *)

Extensions

Data corrected, Offset corrected, Mathematica program corrected and replaced, and b-file replaced by Harvey P. Dale, Feb 01 2024