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Beatty sequence of the real root of 2*x^5 - 9*x^4 + 13*x^3 - 11*x^2 + 5*x - 1; complement of A292987.
1

%I #14 Feb 16 2025 08:33:51

%S 2,5,8,11,13,16,19,22,24,27,30,33,35,38,41,44,46,49,52,55,57,60,63,66,

%T 68,71,74,77,79,82,85,88,90,93,96,99,101,104,107,110,112,115,118,121,

%U 123,126,129,132,134,137,140,143,145,148,151,154,156,159,162,165,167,170,173,176,179

%N Beatty sequence of the real root of 2*x^5 - 9*x^4 + 13*x^3 - 11*x^2 + 5*x - 1; complement of A292987.

%C First differs from A187341 at n = 21.

%C First differs from A108589 at n = 65.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F a(n) = floor(n * r), where r = 2.75393267425618214080...

%e a(2) = floor(2 * 2.7539...) = floor(5.5078...) = 5.

%t r = N[ Root[2#^5 - 9#^4 + 13#^3 - 11#^2 + 5# - 1 &, 1], 64]; Array[ Floor[r #] &, 70] (* _Robert G. Wilson v_, Dec 10 2017 *)

%o (PARI) a(n) = floor(n*solve(x=2, 3, 2*x^5 - 9*x^4 + 13*x^3 - 11*x^2 + 5*x - 1))

%Y Cf. A187341, A108589.

%Y Complement: A292987.

%K nonn,changed

%O 1,1

%A _Iain Fox_, Dec 08 2017