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A083116
Smallest multiple of n using a single digit with multiplicity, or 0 if no such number exists.
3
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.
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
Sequence in context: A069554 A347346 A020485 * A084044 A169930 A048379
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