A244959 Smallest positive multiple of n whose base 8 representation contains only 0's and 1's.

1, 8, 9, 8, 65, 72, 299593, 8, 9, 520, 4169, 72, 65, 2396744, 585, 64, 4097, 72, 513, 520, 17044041, 33352, 33281, 72, 266825, 520, 513, 2396744, 266249, 4680, 4681, 64, 32769, 32776, 16814665, 72, 262145, 4104, 585, 520, 32841, 136352328, 36937, 33352, 585

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=8)
• Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Crossrefs

Cf. A004288 (written in base 8), A004290, A244954-A244960.

Programs

Mathematica

Module[{nn=10,b8},b8=Rest[FromDigits[#,8]&/@Tuples[{0,1},nn]];Table[SelectFirst[ b8,Mod[#,n]==0&],{n,100}]] (* Harvey P. Dale, Feb 03 2024 *)

Python

def A244959(n):
    if n > 0:
        for i in range(1,2**n):
            x = int(bin(i)[2:],8)
            if not x % n:
                return x
    return 0 # Chai Wah Wu, Dec 30 2014

Extensions

Data corrected, offset corrected, and b-file replaced by Harvey P. Dale, Feb 03 2024