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A020987 Zero-one version of Golay-Rudin-Shapiro sequence (or word). 27
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

A word that is uniform primitive morphic, but not pure morphic. - N. J. A. Sloane, Jul 14 2018

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.

Lipshitz, Leonard, and A. van der Poorten. "Rational functions, diagonals, automata and arithmetic." In Number Theory, Richard A. Mollin, ed., Walter de Gruyter, Berlin (1990): 339-358.

LINKS

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

Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807, Nov 29 2017

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.

Aayush Rajasekaran, Narad Rampersad, Jeffrey Shallit, Overpals, Underlaps, and Underpals, In: Brlek S., Dolce F., Reutenauer C., Vandomme É. (eds) Combinatorics on Words, WORDS 2017, Lecture Notes in Computer Science, vol 10432.

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-François 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.

Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.

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 November 15 01:39 EST 2018. Contains 317224 sequences. (Running on oeis4.)