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%I #22 Jun 29 2019 01:46:23
%S 3,0,3,3,3,4,3,5,3,3,3,3,3,3,3,3,3,4,3,4,3,3,3,4,3,4,3,3,3,3,3,3,3,3,
%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,3,5,3,3,3,6,3,6,3,3,3,3,3,3,
%U 3,3,3,4,3,4,3,3,3,4,3,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 1 (or 0 if no such base exists).
%C If we drop the b >= 3 requirement, then this sequence becomes A007395 (the constant 2 sequence).
%C a(n) > 0 for n >= 3 since the base-(n-1) representation of n is 11.
%C a(n)=3 if and only if n is in A081606.
%C The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k with k a prime number.
%C The first n for which a(n)=7 is 560.
%C The first n for which a(n)=8 is 870899850.
%C The first n for which a(n)=10 is 871017138.
%C The first n for which a(n)=11 is 65473886952.
%C The first n for which a(n)=12 is 65473886954.
%H Nathan Fox, <a href="/A270028/b270028.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[SelectFirst[Range[3, 10], DigitCount[n, #, 1] > 0 &], {n, 3, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)
%o (PARI) a(n) = if (n==2, 0, my(b=3); while(!vecsearch(Set(digits(n, b)), 1), b++); b); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A270027, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270038.
%K nonn,base
%O 1,1
%A _Nathan Fox_, Mar 08 2016
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