

A270027


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


12



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 basen representation of n is 10.


LINKS



MATHEMATICA

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


PROG

(PARI) a(n) = if (n < 3, 0, my(b=3); while(vecmin(digits(n, b)), b++); b); \\ Michel Marcus, Mar 10 2016


CROSSREFS

Cf. A069575, A270026, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270037.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



