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).

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, 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, 2, 2, 2, 2

Offset: 1

Author

Nathan Fox, Mar 08 2016

Keywords

• nonn
• base

Comments

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

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.

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

Links

• Nathan Fox, Table of n, a(n) for n = 1..40000
• Eric Weisstein's World of Mathematics, Ternary

Crossrefs

Cf. A117970, A216194.

Programs

Mathematica

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

PARI

a(n) = if (n==1, 0, my(b=2); while(vecmin(digits(n, b)), b++); b); \\ Michel Marcus, Mar 09 2016