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

%I A083117 #15 Jan 23 2024 17:16:22
%S A083117 1,1,1,1,1,1,1,1,1,0,1,37,8547,15873,37,0,65359477124183,37,
%T A083117 5847953216374269,0,37,1,48309178743961352657,37,0,8547,37,15873,
%U A083117 38314176245210727969348659,0,3584229390681,0,1,65359477124183
%N A083117 Smallest k such that k*n contains a single digit with multiplicity, or 0 if no such number exists.
%C A083117 a(n) = 0 if n = 10m, 16m or 25m.
%D A083117 Amarnath Murthy, "On the divisors of the Smarandache Unary sequence," Smarandache Notions Journal, Volume 11, 1-2-3, Spring 2000.
%H A083117 Bo Gyu Jeong, <a href="/A083117/b083117.txt">Table of n, a(n) for n = 1..1000</a>
%H A083117 Bo Gyu Jeong, <a href="/A083117/a083117.cpp.txt">C++ code which computes A083116 and this sequence</a>
%o A083117 (Python)
%o A083117 from itertools import count
%o A083117 def A083117(n):
%o A083117     if not (n%10 and n%16 and n%25): return 0
%o A083117     for l in count(1):
%o A083117         k = (10**l-1)//9
%o A083117         for a in range(1,10):
%o A083117             b, c = divmod(a*k,n)
%o A083117             if not c:
%o A083117                 return b # _Chai Wah Wu_, Jan 23 2024
%Y A083117 Cf. A083116, A083118.
%K A083117 base,nonn
%O A083117 1,12
%A A083117 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 23 2003
%E A083117 a(21) corrected by _Bo Gyu Jeong_, Jun 12 2012
%E A083117 More terms from _Bo Gyu Jeong_, Jun 13 2012