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Search: id:A118716
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| A118716 |
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Number of different ways to represent n in different bases using only decimal digits or characters (0 to 9). |
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+0
2
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| 1, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 28, 29, 30, 29, 29, 31, 30, 30, 31, 31, 31, 31, 31, 32, 33, 31, 31, 34, 33, 32, 33, 33, 33, 34, 33, 34, 35, 33, 33, 36
(list; graph; listen)
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OFFSET
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1,2
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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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a(27) = 23 because the representation of 27 in unary, binary, ternary, quaternary, etc... bases is as follows: 111111111111111111111111111, 11011, 1000, 123, 102, 43, 36, 33, 30, 27, 25, 23, 21, 1D, 1C, 1B, 1A, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, R, R, R, R..... etc.
Of all of these representations, 23 of them contain only decimal digits (or characters).
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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 &, # ]] &]]; Table[f[n], {n, 72}] (*Chandler*)
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CROSSREFS
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Cf. A095425, A095426, A095427, A095428, A095429, A095430, A095431, A095432, A095433.
Sequence in context: A050270 A009041 A077396 this_sequence A004177 A004721 A030544
Adjacent sequences: A118713 A118714 A118715 this_sequence A118717 A118718 A118719
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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), May 24 2006
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EXTENSIONS
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Corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 19 2006
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