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A020987 Zero-one version of Golay-Rudin-Shapiro sequence (or word). 6
0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is (1-A020985(n))/2. See A020985, which is the main entry for this sequence, for more information. N. J. A. Sloane, Jun 06 2012

REFERENCES

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 78.

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

LINKS

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

J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869.

James D. Currie, Narad Rampersad, Kalle Saari, Luca Q. Zamboni, Extremal words in morphic subshifts, Discrete Math. 322 (2014), 53--60. MR3164037. See Sect. 8.

Michael Gilleland, Some Self-Similar Integer Sequences

A. Hof, O. Knill and B. Simon, Singular continuous spectrum for palindromic Schroedinger operators, Commun. Math. Phys. 174 (1995), 149-159.

L. Lipshitz and A. J. van der Poorten, Rational functions, diagonals, automata and arithmetic

H. Niederreiter and M. Vielhaber, Tree complexity and a doubly exponential gap between structured and random sequences, J. Complexity, 12 (1996), 187-198.

Thomas Stoll, On digital blocks of polynomial values and extractions in the Rudin-Shapiro sequence, RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2016, 50, pp. 93-99. <hal-01278708>.

Index entries for characteristic functions

MATHEMATICA

a[n_] := (1/2)*(1-(-1)^Count[Partition[IntegerDigits[n, 2], 2, 1], {1, 1}]); Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, Dec 12 2014, after Robert G. Wilson v *)

PROG

(Haskell)

a020987 = (`div` 2) . (1 -) . a020985  -- Reinhard Zumkeller, Jun 06 2012

CROSSREFS

Cf. A020985.

A014081(n) mod 2. Characteristic function of A022155.

Sequence in context: A060039 A107078 A163533 * A072786 A144597 A125117

Adjacent sequences:  A020984 A020985 A020986 * A020988 A020989 A020990

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 21 02:32 EDT 2017. Contains 289629 sequences.