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

1,1

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A357062 A066851 A288571 * A167223 A341480 A261922

Adjacent sequences: A270025 A270026 A270027 * A270029 A270030 A270031

Keyword

nonn,base

Author

Nathan Fox, Mar 08 2016

Status

approved