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%I #23 Jun 29 2019 01:39:42
%S 0,0,0,0,0,7,0,0,0,0,0,0,7,8,9,10,11,12,13,7,15,8,17,9,19,10,7,11,23,
%T 8,25,13,9,7,29,10,31,8,11,17,7,7,7,7,7,7,7,7,8,8,8,8,8,8,7,9,9,9,9,9,
%U 9,7,10,10,10,10,10,10,7,8,11,11,11,11,11,7,12,8,12,12,12
%N a(n) is the smallest b for which the base-b representation of n contains at least one 6 (or 0 if no such base exists).
%C a(n) > 0 for n >= 13 since 16 is n written in base n-6.
%C The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 6 and k a prime number.
%H Nathan Fox, <a href="/A270032/b270032.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[SelectFirst[Range[7, 1200], DigitCount[n, #, 6] > 0 &], {n, 13, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)
%o (PARI) a(n) = if ((n<13) && (n!=6), 0, my(b=7); while(!vecsearch(Set(digits(n, b)), 6), b++); b); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270042.
%K nonn,base
%O 1,6
%A _Nathan Fox_, Mar 08 2016
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