

A270028


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


11



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
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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(n1) representation of n is 11.
a(n)=3 if and only if n is in A081606.
The only perfect kth 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: A066958 A066851 A288571 * A167223 A261922 A078907
Adjacent sequences: A270025 A270026 A270027 * A270029 A270030 A270031


KEYWORD

nonn,base


AUTHOR

Nathan Fox, Mar 08 2016


STATUS

approved



