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A270035 a(n) is the smallest b for which the base-b representation of n contains at least one 9 (or 0 if no such base exists).

%I A270035 #25 Jun 29 2019 01:39:55
%S A270035 0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,10,11,12,13,14,15,16,17,18,19,
%T A270035 10,21,11,23,12,25,13,27,14,29,10,31,16,11,17,35,12,37,19,13,10,41,14,
%U A270035 43,11,15,23,47,12,49,10,17,13,53,18,11,14,19,29,59,10,61,31,21,16,13,11,67,17,23,10,71
%N A270035 a(n) is the smallest b for which the base-b representation of n contains at least one 9 (or 0 if no such base exists).
%C A270035 a(n) > 0 for n >= 19 since 19 is n written in base n-9.
%C A270035 The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 9 and k a prime number.
%H A270035 Nathan Fox, <a href="/A270035/b270035.txt">Table of n, a(n) for n = 1..10000</a>
%t A270035 Table[SelectFirst[Range[10, 1200], DigitCount[n, #, 9] > 0 &], {n, 19, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)
%o A270035 (PARI) a(n) = if ((n<19) && (n!=9), 0, my(b=10); while(!vecsearch(Set(digits(n, b)), 9), b++); b); \\ _Michel Marcus_, Mar 10 2016
%Y A270035 Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270033, A270034, A270045.
%K A270035 nonn,base
%O A270035 1,9
%A A270035 _Nathan Fox_, Mar 08 2016