A216479 a(n) is the least multiple of n which uses only the digit 1, or a(n) = -1 if no such multiple exists.

1, -1, 111, -1, -1, -1, 111111, -1, 111111111, -1, 11, -1, 111111, -1, -1, -1, 1111111111111111, -1, 111111111111111111, -1, 111111, -1, 1111111111111111111111, -1, -1, -1, 111111111111111111111111111, -1, 1111111111111111111111111111, -1, 111111111111111, -1, 111111, -1, -1, -1, 111, -1, 111111, -1, 11111, -1

Offset: 1

Author

V. Raman, Sep 07 2012

Keywords

• sign
• base

Comments

a(n) = -1 if and only if n is a multiple of 2 or 5. See comment in A216485. - Chai Wah Wu, Jun 21 2015

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A084681 (number of 1's), A190301 (multiplier).

Cf. A004290, A079339, A181060, A181061.

Programs

Mathematica

Array[Which[GCD[#, 10] != 1, -1, Mod[#, 3] == 0, Block[{k = 1}, While[Mod[k, #] != 0, k = 10 k + 1]; k], True, (10^MultiplicativeOrder[10, #] - 1)/9] &, 42] (* Michael De Vlieger, Dec 11 2020 *)

Python

def A216479(n):
    if n % 2 == 0 or n % 5 == 0:
        return -1
    rem = 1
    while rem % n != 0:
        rem = rem*10 + 1
    return rem
# Azanul Haque, Nov 28 2020