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A306494 Smallest number m such that n*3^m has 2 or more identical adjacent decimal digits.

%I A306494 #16 Feb 21 2019 09:49:23
%S A306494 11,8,10,8,11,7,9,5,9,11,0,7,2,4,10,2,4,6,7,8,8,0,5,4,2,9,8,4,6,10,4,
%T A306494 2,0,8,6,6,1,1,1,8,3,3,3,0,9,5,5,1,2,11,3,7,2,5,0,7,6,2,1,7,6,2,7,5,3,
%U A306494 0,6,4,4,9,7,3,5,1,1,1,0,8,2,5,7,3,3,3,1
%N A306494 Smallest number m such that n*3^m has 2 or more identical adjacent decimal digits.
%C A306494 a(n) is smallest m such that 3^m*n is in the sequence A171901 (or -1 if no such m exists).
%C A306494 0 <= a(n) <= 35 for all n > 0. This is proved by showing that for each 0 < n < 10^9, there is a number m <= 35 such that 3^m*n mod 10^9 has adjacent identical digits. If n > 0 and n == 0 mod 10^9, then clearly a(n) = 0.
%H A306494 Chai Wah Wu, <a href="/A306494/b306494.txt">Table of n, a(n) for n = 1..10000</a>
%F A306494 a(A171901(n)) = 0.
%e A306494 a(1) = 11 since 3^11 = 177147 has 2 adjacent digits '7' and no smaller power of 3 has adjacent identical digits.
%e A306494 Record values:
%e A306494 a(1) = 11
%e A306494 a(241) = 12
%e A306494 a(2392) = 14
%e A306494 a(35698) = 15
%e A306494 a(267345) = 16
%e A306494 a(893521) = 17
%e A306494 a(29831625) = 18
%e A306494 a(3232453125) = 19
%o A306494 (Python)
%o A306494 def A306494(n):
%o A306494     m, k= 0, n
%o A306494     while True:
%o A306494         s = str(k)
%o A306494         for i in range(1,len(s)):
%o A306494             if s[i] == s[i-1]:
%o A306494                 return m
%o A306494         m += 1
%o A306494         k *= 3
%Y A306494 Cf. A171901, A306305.
%K A306494 nonn,base
%O A306494 1,1
%A A306494 _Chai Wah Wu_, Feb 19 2019