A036299 Binary Fibonacci (or rabbit) sequence.

1, 10, 101, 10110, 10110101, 1011010110110, 101101011011010110101, 1011010110110101101011011010110110, 1011010110110101101011011010110110101101011011010110101

Offset

0,2

Comments

A055642(a(n)) = A000045(n+2). - Reinhard Zumkeller, Jul 06 2014

References

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.

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.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..14

M. S. El Naschie, Statistical geometry of a Cantor discretum and semiconductors, Computers Math. Applic., 29 (No, 12, 1995), 103-110.

C. J. Glasby, S. P. Glasby and F. Pleijel, Worms by number, Proc. Roy. Soc. B, Proc. Biol. Sci. 275 (1647) (2008) 2071-2076.

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.

Formula

a(n+1) = concatenation of a(n) and a(n-1).

Mathematica

nxt[{a_, b_}]:=FromDigits[Join[IntegerDigits[b], IntegerDigits[a]]]; Transpose[NestList[{Last[#], nxt[#]}&, {1, 10}, 10]][[1]] (* Harvey P. Dale, Oct 16 2011 *)

Prog

(Haskell)
a036299 n = a036299_list !! n
a036299_list = map read rabbits :: [Integer] where
   rabbits = "1" : "10" : zipWith (++) (tail rabbits) rabbits
-- Reinhard Zumkeller, Jul 06 2014
(Python)
def aupton(terms):
  alst = [1, 10]
  while len(alst) < terms: alst.append(int(str(alst[-1]) + str(alst[-2])))
  return alst[:terms]
print(aupton(9)) # Michael S. Branicky, Jan 10 2021

Crossrefs

Cf. A005614, A003849.

Column k=10 of A144287.

Sequence in context: A324083 A162849 A041182 * A061107 A015498 A266283

Adjacent sequences: A036296 A036297 A036298 * A036300 A036301 A036302

Keyword

nonn,easy,nice,base

Author

N. J. A. Sloane

Status

approved