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Search: id:A100729
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| A100729 |
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Period of the first difference of Ulam 1-additive sequence U(2,2n+1). |
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+0
6
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| 32, 26, 444, 1628, 5906, 80, 126960, 380882, 2097152, 1047588, 148814, 8951040, 5406720, 242, 127842440, 11419626400, 12885001946, 160159528116, 687195466408, 6390911336402, 11728121233408, 20104735604736
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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It was proved by Akeran that a(2^k-1) = 3^(k+1) - 1.
Note that a(n)=2^(2n+1) as soon as A100730(n)=2^(2n+3)-2, that happens for n=(m-2)/2 with m>=6 being an even element of A073639.
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LINKS
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Max Alekseyev, Table of n, a(n) for n = 2..31
M. Akeran, On some 1-additive sequences
J. Cassaigne and S. R. Finch, A class of 1-additive sequences and additive recurrences
S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.
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EXAMPLE
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For k=2, we have a(3)=3^3-1=26.
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CROSSREFS
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Cf. A100730 for the fundamental difference, A001857 for U(2, 3), A007300 for U(2, 5), A003668 for U(2, 7).
Sequence in context: A070627 A028697 A161885 this_sequence A070728 A070619 A070626
Adjacent sequences: A100726 A100727 A100728 this_sequence A100730 A100731 A100732
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Dec 03 2004
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EXTENSIONS
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a(3) corrected from 25 to 26 by Hugo van der Sanden (hv(AT)crypt.org) and Bertram Felgenhauer (int-e(AT)gmx.de), Nov 11 2007
More terms from Balakrishnan V (balaji.iitm1(AT)gmail.com), Nov 15 2007
a(21..31) and b-file from Max Alekseyev (maxale(AT)gmail.com), Dec 01 2007
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