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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080764 First differences of A049472, floor(n/sqrt(2)). 13
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Fixed point of the morphism 0->{1}, 1->{1,1,0}. - Benoit Cloitre, May 31 2004

As binary constant 0.1101101110110... = 0.85826765646... (A119812), see Fxtbook link. - Joerg Arndt, May 15 2011

Characteristic word with slope 1/sqrt(2) [J. L. Ramirez et al., arXiv:1212.1368]. - R. J. Mathar, Jul 09 2013

From Peter Bala, Nov 22 2013: (Start)

Sturmian word: equals the limit word S(infinity) where S(0) = 0, S(1) = 1 and for n >= 1, S(n+1) = S(n)S(n)S(n-1).

More generally, for k = 0,1,2,..., we can define a sequence of words S_k(n) by S_k(0) = 0, S_k(1) = 0...01 (k 0's) and for n >= 1, S_k(n+1) = S_k(n)S_k(n)S_k(n-1). Then the limit word S_k(infinity) is a Sturmian word whose terms are given by a(n) = floor((n + 2)/(k + sqrt(2))) - floor((n + 1)/(k + sqrt(2))).

This sequence corresponds to the case k = 0. See A159684 (case k = 1) and A171588 (case k = 2). Compare with the Fibonacci words A005614, A221150, A221151 and A221152. See also A230901. (End)

For n > 0: a(A001951(n)) = 1, a(A001952(n)) = 0. - Reinhard Zumkeller, Jul 03 2015

LINKS

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

Joerg Arndt, Matters Computational (The Fxtbook), section 38.12, pp. 757-758

Wikipedia, Sturmian word

Index entries for sequences that are fixed points of mappings

EXAMPLE

From Peter Bala, Nov 22 2013: (Start)

The first few Sturmian words S(n) are

S(0) = 0

S(1) = 1

S(2) = 110

S(3) = 110 110 1

S(4) = 1101101 1101101 110

S(5) = 11011011101101110 11011011101101110 1101101

The lengths of the words are [1, 1, 3, 7, 17, 41, ...] = A001333.  (End)

MAPLE

A080764 := proc(n)

    alpha := 1/sqrt(2) ;

    floor((n+2)*alpha)-floor((n+1)*alpha) ;

end proc: # R. J. Mathar, Jul 09 2013

MATHEMATICA

Nest[ Flatten[ # /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 7] (* Robert G. Wilson v, Apr 16 2005 *)

NestList[ Flatten[ # /. {0 -> {1}, 1 -> {1, 0, 1}}] &, {1}, 5] // Flatten (* or *)

t = Table[Floor[n/Sqrt[2]], {n, 111}]; Drop[t, 1] - Drop[t, -1] (* Robert G. Wilson v, Nov 03 2005 *)

PROG

(Haskell)

a080764 n = a080764_list !! n

a080764_list = tail $ zipWith (-) (tail a049472_list) a049472_list

-- Reinhard Zumkeller, Jul 03 2015

CROSSREFS

Cf. A005614, A159684, A171588, A221150, A221151, A221152, A230901.

Cf. A049472, A001951, A001952.

Sequence in context: A015923 A014768 A015527 * A014114 A014219 A065828

Adjacent sequences:  A080761 A080762 A080763 * A080765 A080766 A080767

KEYWORD

nonn,easy

AUTHOR

Matthew Vandermast, Mar 25 2003

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 December 11 00:29 EST 2016. Contains 279033 sequences.