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Search: id:A100730
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| A100730 |
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Fundamental difference of Ulam 1-additive sequence starting U(2,2n+1). |
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+0
5
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| 126, 126, 1778, 6510, 23622, 510, 507842, 1523526, 8388606, 4194302, 597870, 35791394, 21691754, 2046, 511305630, 45678505642, 51539607546, 640638112422, 2748779069430, 25563645345606, 46912496118442, 80418967640942
(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) = 2^(2k+3) - 2.
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LINKS
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Max Alekseyev, Table of n, a(n) for n = 2..392
M. Akeran, On some 1-additive sequences
S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.
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FORMULA
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a(n) equals the doubled period of the polynomial x^(2n+2)+x^(2n+1)+1 over GF(2). This polynomial is primitive irreducible as soon as 2n+2 is an element of A073639, implying that for such n, a(n)=2^(2n+3)-2 and A100729(n)=2^(2n+1).
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CROSSREFS
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Cf. A100729 for the period, A001857 for U(2, 3), A007300 for U(2, 5), A003668 for U(2, 7).
Adjacent sequences: A100727 A100728 A100729 this_sequence A100731 A100732 A100733
Sequence in context: A110825 A050451 A059024 this_sequence A044876 A080539 A045167
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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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2 more terms from Balakrishnan V (balaji.iitm1(AT)gmail.com), Nov 15 2007
Further new terms and b-file from Max Alekseyev (maxal(AT)cs.ucsd.edu), Dec 01 2007
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