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| A237665
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Number of partitions of n such that the distinct terms arranged in increasing order form a string of two or more consecutive integers.
(history;
published version)
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#39 by Vaclav Kotesovec at Fri Jan 28 03:20:18 EST 2022
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#38 by Vaclav Kotesovec at Fri Jan 28 03:20:13 EST 2022
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| FORMULA
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a(n) ~ exp(Pi*sqrt(n/3)) / (4*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jan 28 2022
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| STATUS
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approved
editing
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#37 by Susanna Cuyler at Tue Nov 20 16:33:52 EST 2018
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#36 by Michel Marcus at Tue Nov 20 12:57:04 EST 2018
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#35 by Michael De Vlieger at Tue Nov 20 12:47:46 EST 2018
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#34 by Michael De Vlieger at Tue Nov 20 12:47:45 EST 2018
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| LINKS
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Shane Chern (Xiaohang Chen), <a href="https://sites.psu.edu/shanechern/files/2018/07/On-a-conjecture-of-George-Beck-II-2dpatgk.pdf">On a conjecture of George Beck. II</a>, 2018.
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| STATUS
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approved
editing
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#33 by N. J. A. Sloane at Sun May 07 00:58:40 EDT 2017
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#32 by N. J. A. Sloane at Sun May 07 00:58:19 EDT 2017
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| COMMENTS
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Conjecture: a(n+1) = sum of smallest parts in the distinct partitions of n with an even number of parts.. - _George Beck_, May 06 2017
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| STATUS
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proposed
editing
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Discussion
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| Sun May 07
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| N. J. A. Sloane: The conjecture needed to be signed
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#31 by George Beck at Sun May 07 00:52:29 EDT 2017
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#30 by George Beck at Sun May 07 00:52:08 EDT 2017
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| COMMENTS
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Conjecture: A237665a(n+1) = sum of smallest parts in the distinct partitions of n with an even number of parts.
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Discussion
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| Sun May 07
| 00:52
| George Beck: It is a(n+1) now.
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