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

1,3

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A090395 A168485 A276737 * A271726 A350640 A354932

Adjacent sequences: A270024 A270025 A270026 * A270028 A270029 A270030

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved