A270027 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).

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, 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, 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

Offset: 1

Author

Nathan Fox, Mar 08 2016

Keywords

• nonn
• base

Comments

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).

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

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

Links

• Nathan Fox, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = if (n < 3, 0, my(b=3); while(vecmin(digits(n, b)), b++); b); \\ Michel Marcus, Mar 10 2016