A005205 Coding Fibonacci numbers.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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.

Crossrefs

Cf. A005203, A036299.

Column k=3 of A144287.

Programs

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 *)

Extensions

More terms from Jonathan Vos Post, Oct 19 2007

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