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A270030 a(n) is the smallest b for which the base-b representation of n contains at least one 4 (or 0 if no such base exists).

%I A270030 #25 Jun 29 2019 01:39:34
%S A270030 0,0,0,5,0,0,0,0,5,6,7,8,9,5,11,6,13,7,5,5,5,5,5,5,6,6,6,6,5,7,7,7,7,
%T A270030 5,8,8,8,8,5,6,9,9,9,5,5,5,5,5,5,11,11,6,7,5,12,12,12,6,5,6,6,6,6,5,6,
%U A270030 14,7,8,5,5,5,5,5,5,16,6,7,7,5,7,7,6,7,5,9,18,18,6,5,19
%N A270030 a(n) is the smallest b for which the base-b representation of n contains at least one 4 (or 0 if no such base exists).
%C A270030 a(n) > 0 for n >= 9 since 14 is n written in base n-4.
%C A270030 The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k, 3^k, or 4^k, with k a prime number.
%H A270030 Nathan Fox, <a href="/A270030/b270030.txt">Table of n, a(n) for n = 1..10000</a>
%t A270030 Table[SelectFirst[Range[5, 10^3], DigitCount[n, #, 4] > 0 &], {n, 9, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)
%o A270030 (PARI) a(n) = if ((n<9) && (n!=4), 0, my(b=5); while(!vecsearch(Set(digits(n, b)), 4), b++); b); \\ _Michel Marcus_, Mar 10 2016
%Y A270030 Cf. A268236, A268237, A270027, A270028, A216194, A270029, A270031, A270032, A270033, A270034, A270035, A270040.
%K A270030 nonn,base
%O A270030 1,4
%A A270030 _Nathan Fox_, Mar 08 2016