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Search: id:A118868
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| A118868 |
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Smallest number that can be represented in n different ways in n different bases utilizing only decimal characters (0 to 9). |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Is it possible that this sequence is finite?
a(62) > 125000. - Chandler
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LINKS
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Eric Weisstein's World of Mathematics, Base.
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EXAMPLE
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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...
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MATHEMATICA
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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*)
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CROSSREFS
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Cf. A118716, A095425, A095426, A095427, A095428.
Sequence in context: A011879 A011878 A017896 this_sequence A017885 A011874 A000115
Adjacent sequences: A118865 A118866 A118867 this_sequence A118869 A118870 A118871
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KEYWORD
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base,nonn
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AUTHOR
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Sergio Pimentel (ferdiego(AT)cox.net), Jun 13 2006
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EXTENSIONS
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a(55)-a(61) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 19 2006
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