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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).
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
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.
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
KEYWORD
nonn,base
AUTHOR
Nathan Fox, Mar 08 2016
STATUS
approved