The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A116178 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A116178

Stewart's choral sequence: a(3n) = 0, a(3n-1) = 1, a(3n+1) = a(n).
(history; published version)

#39 by Michael De Vlieger at Thu Dec 23 10:03:37 EST 2021

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reviewed

approved

#38 by Andrew Howroyd at Thu Dec 23 09:44:23 EST 2021

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proposed

reviewed

#37 by Michel Marcus at Thu Dec 23 00:55:50 EST 2021

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editing

proposed

#36 by Michel Marcus at Thu Dec 23 00:55:46 EST 2021

LINKS

Gabriele Fici and Jeffrey Shallit, <a href="https://arxiv.org/abs/2112.12125">Properties of a Class of Toeplitz Words</a>, arXiv:2112.12125 [cs.FL], 2021.

STATUS

approved

editing

#35 by Peter Luschny at Fri Jul 03 14:43:29 EDT 2020

STATUS

editing

approved

#34 by Peter Luschny at Fri Jul 03 14:43:19 EDT 2020

CROSSREFS

Cf. A010060, A189636, A189637, A189638, A121894.

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proposed

editing

#33 by Wesley Ivan Hurt at Fri Jul 03 13:41:16 EDT 2020

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editing

proposed

#32 by Wesley Ivan Hurt at Fri Jul 03 13:41:01 EDT 2020

FORMULA

a(3n3*n) = 0, a(3n3*n-1) = 1 and a(3n3*n+1) = a(n).

G.f.: x^2/(1-x^3) +x^7/(1-x^9) +x^22/(1-x^27) +... . a(-1-n) = 1-a(n). - Michael Somos, Apr 17 2007

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proposed

editing

#31 by Omar E. Pol at Fri Jul 03 12:44:16 EDT 2020

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editing

proposed

#30 by Omar E. Pol at Fri Jul 03 12:44:05 EDT 2020

COMMENTS

Van der Waerden's theorem tells us there can be no infinite binary word avoiding a monochromatic arithmetic progression of length 5 (the longest is of length 177; see A121894). However, Stewart's choral sequence has the property that it has no ababa appearing in arithmetic progression, for a different from b. - Jeffrey Shallit, Jul 03 2020

STATUS

proposed

editing