A270028 a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 1 (or 0 if no such base exists).

3, 0, 3, 3, 3, 4, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 5, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 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

If we drop the b >= 3 requirement, then this sequence becomes A007395 (the constant 2 sequence).

a(n) > 0 for n >= 3 since the base-(n-1) representation of n is 11.

a(n)=3 if and only if n is in A081606.

The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k with k a prime number.

The first n for which a(n)=7 is 560.

The first n for which a(n)=8 is 870899850.

The first n for which a(n)=10 is 871017138.

The first n for which a(n)=11 is 65473886952.

The first n for which a(n)=12 is 65473886954.

Links

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

Crossrefs

Cf. A270027, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270038.

Programs

Mathematica

Table[SelectFirst[Range[3, 10], DigitCount[n, #, 1] > 0 &], {n, 3, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

PARI

a(n) = if (n==2, 0, my(b=3); while(!vecsearch(Set(digits(n, b)), 1), b++); b); \\ Michel Marcus, Mar 10 2016