A004287 Least positive multiple of n written in base 7 using only 0 and 1.

1, 11, 111, 11, 101, 111111, 10, 11, 1011, 101, 10011, 111111, 1011, 110, 11001, 1111, 100111, 1101111, 111, 1111, 1110, 11101, 101011, 111111, 101, 111001, 1011, 110, 1111111, 1011111, 100111, 11011, 10011, 100111, 1010, 1101111

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A244958 (written in base 10).

Programs

Mathematica

With[{cl=Rest[{FromDigits[#,7],FromDigits[#]}&/@Tuples[{0,1},7]]},Table[ SelectFirst[ cl,Mod[#[[1]],n]==0&],{n,40}]][[;;,2]] (* Harvey P. Dale, Jan 31 2024 *)

Python

def A004287(n):
    if n > 0:
        for i in range(1,2**n):
            s = bin(i)[2:]
            if not int(s,7) % n:
                return int(s)
    return 0 # Chai Wah Wu, Dec 30 2014

Extensions

Removed initial 0 since (1) it did not match the definition, and (2) there are many similar sequences with the same author which also say "positive". Also changed offset. - N. J. A. Sloane, Jan 31 2024

Previous b-file replaced by Harvey P. Dale, Jan 31 2024