The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A359228 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A359228

Number of states in the minimal deterministic finite automaton with output generating the n-fold running sum (mod 2) of the Thue-Morse sequence (A010060).
(history; published version)

#28 by N. J. A. Sloane at Sat May 20 16:28:08 EDT 2023

STATUS

proposed

approved

#27 by Sean A. Irvine at Fri Apr 21 18:13:58 EDT 2023

STATUS

editing

proposed

#26 by Sean A. Irvine at Fri Apr 21 18:13:50 EDT 2023

FORMULA

a(2^n) = 2^(n+3). (Proof in Shallit and Zavyalov.) . - Anatoly Zavyalov, Mar 30 2023

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proposed

editing

#25 by Jon E. Schoenfield at Sun Apr 02 08:45:31 EDT 2023

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Sun Apr 02 08:45:13 EDT 2023

FORMULA

a(2^n) = 2^(n+3). (Proof in Shallit and Zavyalov). ) - Anatoly Zavyalov, Mar 30 2023

STATUS

proposed

editing

#23 by Michel Marcus at Sun Apr 02 04:21:54 EDT 2023

STATUS

editing

proposed

#22 by Michel Marcus at Sun Apr 02 04:21:36 EDT 2023

FORMULA

a(2^n) = 2^(n+3). (Proof in Jeffrey Shallit and Anatoly Zavyalov, <a href="https://arxiv.org/abs/2303.15203">Transduction of Automatic Sequences and Applications</a>, arXiv:2303.15203 [cs.FL], 2023, see p. 21) . - Anatoly Zavyalov, Mar 30 2023

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proposed

editing

#21 by Anatoly Zavyalov at Sat Apr 01 17:44:12 EDT 2023

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editing

proposed

#20 by Anatoly Zavyalov at Sat Apr 01 17:42:53 EDT 2023

COMMENTS

The 0-fold running sum of A010060 is A010060. To generate the n-fold running sum {c(nk) } from the (n-1)-fold running sum {b(nk), }, define c(0) = b(0) and c(nk+1) = (c(nk) + b(nk+1) () mod 2).

STATUS

proposed

editing

#19 by Michel Marcus at Fri Mar 31 01:23:50 EDT 2023

STATUS

editing

proposed

Discussion

Sat Apr 01

10:24

Anatoly Zavyalov: Yes, thank you.