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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014707 a(4n)=0, a(4n+2)=1, a(2n+1)=a(n). 18
0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The regular paper-folding (or dragon curve) sequence.

It appears that the sequence of run lengths is A088431. - Dimitri Hendriks, May 06 2010

Runs of three consecutive ones appear around positions n = 22, 46, 54, 86, 94, 118, 150, 174, 182,..., or for n of the form 2^(k+3)*(4*t+3)-2, k>=0, t>=0. - Vladimir Shevelev, Mar 19 2011

a(A091072(n)+1) = 0; a(A091067(n)+1) = 1. - Reinhard Zumkeller, Sep 28 2011

REFERENCES

G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.

LINKS

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

J.-P. Allouche, M. Mendes France, A. Lubiw, A.J. van der Poorten and J. Shallit, Convergents of folded continued fractions

G. J. Endrullis, D. Hendriks and J. W. Klop, Degrees of streams

J.-Y. Kao et al., Words avoiding repetitions in arithmetic progressions

G. Melancon, Home page

G. Melancon, Lyndon factorization of infinite words, STACS 96 (Grenoble, 1996), 147-154, Lecture Notes in Comput. Sci., 1046, Springer, Berlin, 1996. Math. Rev. 98h:68188.

Index entries for sequences obtained by enumerating foldings

FORMULA

a(4n)=0, a(4n+2)=1, a(2n+1)=a(n).

a(n) = (1-jacobi(-1,n))/2 (cf. A034947). - N. J. A. Sloane, Jul 27 2012

Set a=0, b=1, S(0)=a, S(n+1) = S(n)aF(S(n)), where F(x) reverses x and then interchanges a and b; sequence is limit S(infinity).

a((2*n+1)*2^p-1) = n mod 2, p >= 0. - Johannes W. Meijer, Jan 28 2013

MAPLE

nmax:=92: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 0 to ceil(nmax/(p+2))+1 do a((2*n+1)*2^p-1) := n mod 2 od: od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Jan 28 2013

MATHEMATICA

a[n_ /; Mod[n, 4] == 0] = 0; a[n_ /; Mod[n, 4] == 2] = 1; a[n_ /; Mod[n, 2] == 1] := a[n] = a[(n - 1)/2]; Table[a[n], {n, 0, 92}] (* Jean-Fran├žois Alcover, May 17 2011 *)

PROG

(Haskell)

a014707 n = a014707_list !! n

a014707_list = f 0 $ cycle [0, 0, 1, 0] where

   f i (x:_:xs) = x : a014707 i : f (i+1) xs

-- Reinhard Zumkeller, Sep 28 2011

CROSSREFS

Equals 1 - A014577, which see for further references. Also a(n) = A038189(n+1).

The following are all essentially the same sequence: A014577, A014707, A014709, A014710, A034947, A038189, A082410.

Cf. A220466

Sequence in context: A028999 A091244 A131378 * A106138 A064990 A059125

Adjacent sequences:  A014704 A014705 A014706 * A014708 A014709 A014710

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Scott C. Lindhurst (ScottL(AT)alumni.princeton.edu)

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 March 27 16:36 EDT 2017. Contains 284177 sequences.