

A118868


Smallest number that can be represented in n different ways in n different bases utilizing only decimal characters (0 to 9).


0



1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 42, 45, 48, 56, 57, 60, 69, 72, 81, 84, 93, 105, 105, 144, 144, 177, 216, 225, 225, 288, 441, 513, 513, 729, 1224, 1800, 2304, 2304, 4761, 4761, 11664, 11664, 11664
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OFFSET

1,2


COMMENTS

Is it possible that this sequence is finite?
a(62) > 125000.  Chandler


LINKS

Table of n, a(n) for n=1..61.
Eric Weisstein's World of Mathematics, Base.


EXAMPLE

E.g. a(3)=2 because 2 is the smaller number that can be represented in 3 different ways using decimal characters (11 in unary, 10 in binary and 2 in ternary and higher).
a(43)=144 because 144 is the smallest number that can be represented in 43 different ways(using only decimal characters), like 144=10010000 in binary, 144=220 in octal, 144=99 in base 15, 144=20 in base 72, etc...


MATHEMATICA

f[n_] := 1 + If[n == 1, 0, Length@Select[Table[IntegerDigits[n, b], {b, 2, n + 1}], Apply[And, Map[ # < 10 &, # ]] &]]; \ a = {}; k = 1; Do[While[f[k] < n, k++ ]; AppendTo[a, k]; , {n, 61}]; a (*Chandler*)


CROSSREFS

Cf. A118716, A095425, A095426, A095427, A095428.
Sequence in context: A011879 A011878 A017896 * A017885 A274165 A011874
Adjacent sequences: A118865 A118866 A118867 * A118869 A118870 A118871


KEYWORD

base,nonn


AUTHOR

Sergio Pimentel, Jun 13 2006


EXTENSIONS

a(55)a(61) from Ray Chandler, Jun 19 2006


STATUS

approved



