%I #24 Jun 29 2019 01:46:28

%S 0,0,3,4,5,3,7,4,3,3,3,3,13,7,3,4,4,3,3,3,3,11,23,3,5,5,3,3,3,3,3,3,3,

%T 3,3,3,3,3,3,4,6,3,43,4,3,3,3,3,4,4,3,4,5,3,3,3,3,3,3,3,3,3,3,3,3,3,4,

%U 4,3,4,4,3,3,3,3,4,4,3,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).

%C It is natural to consider this sequence starting from base 3 instead of base 2, as the latter causes most terms to be 2 (see A270026).

%C a(n) = n if and only if n = 3 or n is in A069575.

%C a(n) > 0 for n >= 3 since the base-n representation of n is 10.

%H Nathan Fox, <a href="/A270027/b270027.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[SelectFirst[Range[3, 10^3], DigitCount[n, #, 0] > 0 &], {n, 3, 120}] (* _Michael De Vlieger_, Mar 10 2016, Version 10 *)

%o (PARI) a(n) = if (n < 3, 0, my(b=3); while(vecmin(digits(n, b)), b++); b); \\ _Michel Marcus_, Mar 10 2016

%Y Cf. A069575, A270026, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270037.

%K nonn,base

%O 1,3

%A _Nathan Fox_, Mar 08 2016