A270027 - OEIS

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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

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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