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Search: id:A080019
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| A080019 |
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Positive integers such that the smallest real solution to x^n + x = 2Pi*a(n) forms a monotonically increasing sequence as n grows. |
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+0
1
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| 1, 2, 4, 9, 20, 45, 101, 226, 506, 1133, 2538, 5680, 12722, 28494, 63819, 142937, 320140, 717027
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Solutions satisfy cos(x^n)=cos(x), the limit of the smallest real root also being the limit of a(n+1)/a(n) -> 2.2397...
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EXAMPLE
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Smallest real roots r(n) of equation x^n + x = a(n)(2Pi), for n=2...8, are: x^2 + x = 1(2Pi), r(2)=2.0560009...; x^3 + x = 2(2Pi), r(3)=2.1817119...; x^4 + x = 4(2Pi), r(4)=2.1886076...; x^5 + x = 9(2Pi), r(5)=2.2233125...; x^6 + x = 20(2Pi), r(6)=2.2313694...; x^7 + x = 45(2Pi), r(7)=2.2372063...; x^8 + x = 101(2Pi), r(8)=2.2393436...
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CROSSREFS
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Sequence in context: A091620 A108469 A085584 this_sequence A052534 A080135 A167750
Adjacent sequences: A080016 A080017 A080018 this_sequence A080020 A080021 A080022
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Jan 20 2003
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