A005205 Coding Fibonacci numbers. (Formerly M2877)

1, 3, 10, 93, 2521, 612696, 4019900977, 6409020585966267, 67040619014505181883304178, 1118048584563024433220786501983631190591549, 195042693446883195450571898296824337898272003171567594807867055549521

Offset

1,2

Comments

Binary Fibonacci (or rabbit) sequence A036299, read in base 3, then converted to decimal. - Jonathan Vos Post, Oct 19 2007

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..16

H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., Sequences associated with t-ary coding of Fibonacci's rabbits, Fib. Quart., 15 (1977), 311-318.

Example

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.

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A005203, A036299.

Column k=3 of A144287.

Sequence in context: A135457 A225505 A073733 * A216450 A181079 A240512

Adjacent sequences: A005202 A005203 A005204 * A005206 A005207 A005208

Keyword

nonn,base

Author

N. J. A. Sloane

Extensions

More terms from Jonathan Vos Post, Oct 19 2007

Corrected (a(4) was missing) and extended by Alois P. Heinz, Sep 17 2008

Status

approved