login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005713 Define strings S(0)=0, S(1)=11, S(n) = S(n-1)S(n-2); iterate. 4
1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(A035336(n)) = 0. [Reinhard Zumkeller, Dec 30 2011]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

R. K. Guy, Letter to N. J. A. Sloane, 1987

FORMULA

For n>1, a(n-1)=floor(phi*ceiling(n/phi))-ceiling(phi*floor(n/phi)) where phi=(1+sqrt(5))/2. For n>=0, a(n)=abs(A005713(n+1)). - Benoit Cloitre, Apr 21 2003

EXAMPLE

The infinite word is S(infinity) = 110111101101111011110110...

MATHEMATICA

s[0] = {0}; s[1] = {1, 1}; s[n_] := s[n] = Join[s[n-1], s[n-2]]; s[10] (* Jean-Fran├žois Alcover, May 15 2013 *)

PROG

(PARI) a(n, f1, f2)=local(f3); for(i=3, n, f3=concat(f2, f1); f1=f2; f2=f3); f2

(PARI) printp(a(10, [ 0 ], [ 1, 1 ])) \\ Would give S(10). Sequence is S(infinity).

(Haskell)

a005713 n = a005713_list !! n

a005713_list = 1 : 1 : concat (sibb [0] [1, 1]) where

   sibb xs ys = zs : sibb ys zs where zs = xs ++ ys

-- Reinhard Zumkeller, Dec 30 2011

CROSSREFS

Cf. A005614, A003849.

Sequence in context: A118828 A105234 A181183 * A085241 A105368 A138019

Adjacent sequences:  A005710 A005711 A005712 * A005714 A005715 A005716

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected by Michael Somos

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 08:37 EDT 2018. Contains 316259 sequences. (Running on oeis4.)