Revisions by Jeffrey Shallit
(See also Jeffrey Shallit's wiki page)
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#147 by Jeffrey Shallit at Wed Jul 10 06:48:46 EDT 2024
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#146 by Jeffrey Shallit at Wed Jul 10 06:48:39 EDT 2024
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Numbers with Tribonacci representation that is a prefix of 100100100100... . - Jeffrey Shallit, Jul 10 2024
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approved
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#6 by Jeffrey Shallit at Tue Jul 09 10:52:58 EDT 2024
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#5 by Jeffrey Shallit at Tue Jul 09 10:52:55 EDT 2024
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Jamie Simpson, <a href="https://arxiv.org/abs/2402.05381">Palindromic periodicities</a>, ArXiv preprint arXiv:2402.05381 [math.CO], May 1 2024.
arXiv:2402.05381 [math.CO], May 1 2024.
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proposed
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#4 by Jeffrey Shallit at Tue Jul 09 10:52:33 EDT 2024
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#3 by Jeffrey Shallit at Tue Jul 09 10:52:30 EDT 2024
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2, 4, 8, 16, 32, 58, 108, 190, 336, 560, 948, 1574, 2568, 4116, 6596, 10444, 16320, 25488, 39216, 60690, 92204
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#2 by Jeffrey Shallit at Tue Jul 09 10:46:07 EDT 2024
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allocatedNumber of palindromic periodicities among the binary words forof Jeffreylength Shallitn.
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2, 4, 8, 16, 32, 58, 108, 190, 336, 560, 948, 1574, 2568, 4116, 6596, 10444, 16320, 25488, 39216, 60690
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| OFFSET
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1,1
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| COMMENTS
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A binary word w is a "palindromic periodicity" if it is the prefix of the infinite word pspsps... where p and s are palindromes, not both empty, and w is at least as long as ps.
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Jamie Simpson, <a href="https://arxiv.org/abs/2402.05381">Palindromic periodicities</a>, ArXiv preprint
arXiv:2402.05381 [math.CO], May 1 2024.
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| EXAMPLE
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For n = 6, the six binary words that are not palindromic periodicities are 001011, 001101, 010011, 101100, 110010, 110100.
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allocated
nonn
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| AUTHOR
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Jeffrey Shallit, Jul 09 2024
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approved
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#1 by Jeffrey Shallit at Tue Jul 09 10:46:07 EDT 2024
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allocated for Jeffrey Shallit
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allocated
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approved
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| A372846
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a(n) is the number of states in the smallest deterministic finite automaton that accepts the Zeckendorf representation of i and n*i, in parallel, for all integers i>=0.
(history;
published version)
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#12 by Jeffrey Shallit at Sun Jul 07 06:11:20 EDT 2024
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Discussion
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| Sun Jul 07
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| Kevin Ryde: Hmm. That "Numbers k" is right for a list type sequence, of numbers chosen by a property -- as opposed to a function of the index n.
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| 13:55
| N. J. A. Sloane: Kevin is right.
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#11 by Jeffrey Shallit at Sun Jul 07 06:11:15 EDT 2024
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a(kn) is the number of states in the smallest deterministic finite automaton that accepts the Zeckendorf representation of ni and k*n*i, in parallel, for all integers ni>=0.
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Conjecture: a(kn) <= 2*kn^2 + g^2*kn + 1, where g = (1+sqrt(5))/2.
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