A083117 Smallest k such that k*n contains a single digit with multiplicity, or 0 if no such number exists.

1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 37, 8547, 15873, 37, 0, 65359477124183, 37, 5847953216374269, 0, 37, 1, 48309178743961352657, 37, 0, 8547, 37, 15873, 38314176245210727969348659, 0, 3584229390681, 0, 1, 65359477124183

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 23 2003

Keywords

• base
• nonn

Comments

a(n) = 0 if n = 10m, 16m or 25m.

References

• Amarnath Murthy, "On the divisors of the Smarandache Unary sequence," Smarandache Notions Journal, Volume 11, 1-2-3, Spring 2000.

Links

• Bo Gyu Jeong, Table of n, a(n) for n = 1..1000
• Bo Gyu Jeong, C++ code which computes A083116 and this sequence

Crossrefs

Cf. A083116, A083118.

Programs

Python

from itertools import count
def A083117(n):
    if not (n%10 and n%16 and n%25): return 0
    for l in count(1):
        k = (10**l-1)//9
        for a in range(1,10):
            b, c = divmod(a*k,n)
            if not c:
                return b # Chai Wah Wu, Jan 23 2024

Extensions

a(21) corrected by Bo Gyu Jeong, Jun 12 2012

More terms from Bo Gyu Jeong, Jun 13 2012