Search: id:A118868
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%I A118868
%S A118868 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,
%T A118868 39,42,45,48,56,57,60,69,72,81,84,93,105,105,144,144,177,216,225,225,
%U A118868 288,441,513,513,729,1224,1800,2304,2304,4761,4761,11664,11664,11664
%N A118868 Smallest number that can be represented in n different ways in n different 
               bases utilizing only decimal characters (0 to 9).
%C A118868 Is it possible that this sequence is finite?
%C A118868 a(62) > 125000. - Chandler
%H A118868 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Base.html">Base.</a>
%e A118868 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).
%e A118868 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...
%t A118868 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*)
%Y A118868 Cf. A118716, A095425, A095426, A095427, A095428.
%Y A118868 Sequence in context: A011879 A011878 A017896 this_sequence A017885 A011874 
               A000115
%Y A118868 Adjacent sequences: A118865 A118866 A118867 this_sequence A118869 A118870 
               A118871
%K A118868 base,nonn
%O A118868 1,2
%A A118868 Sergio Pimentel (ferdiego(AT)cox.net), Jun 13 2006
%E A118868 a(55)-a(61) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 19 
               2006

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