A270026 - OEIS

%I #26 Jun 29 2019 01:46:20

%S 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 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 2,2,2,2

%N 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 For n > 1, a(n)=2 whenever n+1 is not a power of 2.

%C 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 a(n) > 0 for n >= 2 since the base-n representation of n is 10.

%H Nathan Fox, <a href="/A270026/b270026.txt">Table of n, a(n) for n = 1..40000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Ternary.html">Ternary</a>

%t Table[SelectFirst[Range[2, 1200], DigitCount[n, #, 0] > 0 &], {n, 2, 120}] (* _Michael De Vlieger_, Mar 09 2016, Version 10 *)

%o (PARI) a(n) = if (n==1, 0, my(b=2); while(vecmin(digits(n, b)), b++); b); \\ _Michel Marcus_, Mar 09 2016

%Y Cf. A117970, A216194.

%K nonn,base

%O 1,2

%A _Nathan Fox_, Mar 08 2016