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A005205
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Coding Fibonacci numbers.
(Formerly M2877)
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4
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1, 3, 10, 93, 2521, 612696, 4019900977, 6409020585966267, 67040619014505181883304178, 1118048584563024433220786501983631190591549, 195042693446883195450571898296824337898272003171567594807867055549521
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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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Binary Fibonacci (or rabbit) sequence A036299, read in base 3, then converted to decimal. - Jonathan Vos Post, Oct 19 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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a(0) = 1 because A036299(0) = "1" and 1 base 3 = 1 base 10.
a(1) = 3 because A036299(1) = "10" and 10 base 3 = 3 base 10.
a(2) = 10 because A036299(2) = "101" and 101 base 3 = 10 base 10.
a(3) = 93 because A036299(3) = "10110" and 10110 base 3 = 93 base 10.
a(4) = 2521 because A036299(4) = "10110101" and 10110101 base 3 = 2521 base 10.
a(5) = 612696 because A036299(5) = "1011010110110" and 1011010110110 base 3 = 612696 base 10.
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MAPLE
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b:= proc(n) option remember; `if` (n<2, [n, n], [b(n-1)[1] *3^b(n-1)[2] +b(n-2)[1], b(n-1)[2] +b(n-2)[2]]) end: a:= n-> b(n)[1]: seq(a(n), n=1..11); # Alois P. Heinz, Sep 17 2008
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MATHEMATICA
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b[0] = {1}; b[1] = {1, 0}; b[n_] := b[n] = Join[b[n-1], b[n-2]]; a[n_] := FromDigits[b[n], 3]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Apr 24 2014 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Corrected (a(4) was missing) and extended by Alois P. Heinz, Sep 17 2008
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STATUS
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approved
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