A329792 Smallest positive k such that k*n contains only the digits 1,2,3,4,5, or -1 if no such k exists.

-1, 1, 1, 1, 1, 1, 2, 2, 3, 5, -1, 1, 1, 1, 1, 1, 2, 2, 3, 6, -1, 1, 1, 1, 1, 1, 2, 2, 4, 5, -1, 1, 1, 1, 1, 1, 4, 3, 3, 6, -1, 1, 1, 1, 1, 1, 7, 3, 3, 5, -1, 1, 1, 1, 1, 1, 2, 2, 4, 6, -1, 2, 2, 4, 8, 5, 2, 2, 8, 5, -1, 2, 2, 7, 3, 3, 2, 2, 3, 7, -1, 3, 16, 4, 3, 3, 4, 5, 4, 5, -1

Offset: 0

Author

N. J. A. Sloane, Dec 03 2019

Keywords

• sign
• look
• base

Comments

a(n) > 0 iff n is not a multiple of 10.

References

• G. Galperin and Y. J. Ionin (Proposers), and M. Reid (Solver), Problem 12034, Amer. Math. Monthly, 126:10, 950-951, Dec. 2019.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..25000

Crossrefs

Cf. A084545, A329793.

Programs

Python

def A329792(n):
    if n % 10:
        m, s = 1, set('12345')
        while not set(str(m*n)) <= s:
            m += 1
        return m
    else:
        return -1 # Chai Wah Wu, Dec 04 2019