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A270026 a(n) is the smallest b for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).

%I A270026 #27 Feb 16 2025 08:33:30
%S A270026 0,2,3,2,2,2,7,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,
%T A270026 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,
%U A270026 2,2,2,2
%N A270026 a(n) is the smallest b for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).
%C A270026 For n > 1, a(n)=2 whenever n+1 is not a power of 2.
%C A270026 It is conjectured that the only terms that are neither 2 nor 3 in this sequence are a(7) and a(32767), which are 7 and 5 respectively.
%C A270026 a(n) > 0 for n >= 2 since the base-n representation of n is 10.
%H A270026 Nathan Fox, <a href="/A270026/b270026.txt">Table of n, a(n) for n = 1..40000</a>
%H A270026 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ternary.html">Ternary</a>
%t A270026 Table[SelectFirst[Range[2, 1200], DigitCount[n, #, 0] > 0 &], {n, 2, 120}] (* _Michael De Vlieger_, Mar 09 2016, Version 10 *)
%o A270026 (PARI) a(n) = if (n==1, 0, my(b=2); while(vecmin(digits(n, b)), b++); b); \\ _Michel Marcus_, Mar 09 2016
%Y A270026 Cf. A117970, A216194.
%K A270026 nonn,base
%O A270026 1,2
%A A270026 _Nathan Fox_, Mar 08 2016