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

1,2

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

Mathematica

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

Prog

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

Crossrefs

Cf. A117970, A216194.

Sequence in context: A373249 A077199 A145390 * A340703 A128049 A104543

Adjacent sequences: A270023 A270024 A270025 * A270027 A270028 A270029

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved