cp's OEIS Frontend

A036299 Binary Fibonacci (or rabbit) sequence.

%I A036299 #35 Jan 05 2025 19:51:35
%S A036299 1,10,101,10110,10110101,1011010110110,101101011011010110101,
%T A036299 1011010110110101101011011010110110,
%U A036299 1011010110110101101011011010110110101101011011010110101
%N A036299 Binary Fibonacci (or rabbit) sequence.
%C A036299 A055642(a(n)) = A000045(n+2). - _Reinhard Zumkeller_, Jul 06 2014
%D A036299 N. G. De Bruijn, (1989, January). Updown generation of Beatty sequences.  Koninklijke Nederlandsche Akademie van Wetenschappen (Indationes Math.), Proc., Ser. A, 92:4 (1968), 385-407. See Fig. 3.
%D A036299 J. Kappraff, D. Blackmore and G. Adamson, Phyllotaxis as a dynamical system: a study in number, Chap. 17 of Jean and Barabe, eds., Symmetry in Plants, World Scientific, Studies in Math. Biology and Medicine, Vol. 4.
%H A036299 Reinhard Zumkeller, <a href="/A036299/b036299.txt">Table of n, a(n) for n = 0..14</a>
%H A036299 M. S. El Naschie, <a href="http://dx.doi.org/10.1016/0898-1221(95)00062-4">Statistical geometry of a Cantor discretum and semiconductors</a>, Computers Math. Applic., 29 (No, 12, 1995), 103-110.
%H A036299 C. J. Glasby, S. P. Glasby and F. Pleijel, <a href="http://dx.doi.org/10.1098/rspb.2008.0418">Worms by number</a>, Proc. Roy. Soc. B, Proc. Biol. Sci. 275 (1647) (2008) 2071-2076.
%H A036299 H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-4/gould.pdf">Sequences associated with t-ary coding of Fibonacci's rabbits</a>, Fib. Quart., 15 (1977), 311-318.
%F A036299 a(n+1) = concatenation of a(n) and a(n-1).
%t A036299 nxt[{a_,b_}]:=FromDigits[Join[IntegerDigits[b],IntegerDigits[a]]]; Transpose[NestList[{Last[#],nxt[#]}&,{1,10},10]][[1]] (* _Harvey P. Dale_, Oct 16 2011 *)
%o A036299 (Haskell)
%o A036299 a036299 n = a036299_list !! n
%o A036299 a036299_list = map read rabbits :: [Integer] where
%o A036299    rabbits = "1" : "10" : zipWith (++) (tail rabbits) rabbits
%o A036299 -- _Reinhard Zumkeller_, Jul 06 2014
%o A036299 (Python)
%o A036299 def aupton(terms):
%o A036299   alst = [1, 10]
%o A036299   while len(alst) < terms: alst.append(int(str(alst[-1]) + str(alst[-2])))
%o A036299   return alst[:terms]
%o A036299 print(aupton(9)) # _Michael S. Branicky_, Jan 10 2021
%Y A036299 Cf. A005614, A003849.
%Y A036299 Column k=10 of A144287.
%K A036299 nonn,easy,nice,base
%O A036299 0,2
%A A036299 _N. J. A. Sloane_