A083116 Smallest multiple of n using a single digit with multiplicity, or 0 if no such number exists.

1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 444, 111111, 222222, 555, 0, 1111111111111111, 666, 111111111111111111, 0, 777, 22, 1111111111111111111111, 888, 0, 222222, 999, 444444, 1111111111111111111111111111, 0, 111111111111111, 0, 33, 2222222222222222, 555555

Offset

1,2

Comments

1. If p is a prime > 5 then there exists a d such that a(p) = concatenation of '1' d times where p = k*d + 1 for some k. a(p)= (10^d -1)/9 < ={10^(p-1)- 1}/9.

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

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 A083117 and this sequence

Prog

(Python)
from itertools import count
def A083116(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):
            if not (m:=a*k)%n:
                return m # Chai Wah Wu, Jan 23 2024

Crossrefs

Cf. A083117, A083118.

Sequence in context: A069554 A347346 A020485 * A084044 A169930 A048379

Adjacent sequences: A083113 A083114 A083115 * A083117 A083118 A083119

Keyword

base,nonn

Author

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

Extensions

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

More terms from Bo Gyu Jeong, Jun 13 2012

Status

approved