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A080019 Positive integers such that the smallest real solution to x^n + x = 2*Pi*a(n) forms a monotonically increasing sequence as n grows. 0
1, 2, 4, 9, 20, 45, 101, 226, 506, 1133, 2538, 5680, 12722, 28494, 63819, 142937, 320140, 717027 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

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...

LINKS

Table of n, a(n) for n=2..19.

EXAMPLE

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...

CROSSREFS

Sequence in context: A208738 A108469 A085584 * A052534 A213411 A080135

Adjacent sequences:  A080016 A080017 A080018 * A080020 A080021 A080022

KEYWORD

nonn,more

AUTHOR

Benoit Cloitre and Paul D. Hanna, Jan 20 2003

STATUS

approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)