%I #23 Jun 29 2019 01:39:47
%S 0,0,0,0,0,0,8,0,0,0,0,0,0,0,8,9,10,11,12,13,14,15,8,17,9,19,10,21,11,
%T 23,8,25,13,9,14,29,10,31,8,11,17,35,9,37,19,13,8,41,14,43,11,9,23,47,
%U 8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,8,10,10,10,10,10,10,10,8,11,11
%N a(n) is the smallest b for which the base-b representation of n contains at least one 7 (or 0 if no such base exists).
%C a(n) > 0 for n >= 15 since 17 is n written in base n-7.
%C The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 7 and k a prime number.
%H Nathan Fox, <a href="/A270033/b270033.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[SelectFirst[Range[8, 1200], DigitCount[n, #, 7] > 0 &], {n, 15, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)
%o (PARI) a(n) = if ((n<15) && (n!=7), 0, my(b=8); while(!vecsearch(Set(digits(n, b)), 7), b++); b); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270034, A270035, A270043.
%K nonn,base
%O 1,7
%A _Nathan Fox_, Mar 08 2016