A036299 - OEIS

A036299

Binary Fibonacci (or rabbit) sequence.

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

(list; graph; refs; listen; history; text; internal format)

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