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Beatty sequence for (5-sqrt(3))/2.
2

%I #14 Sep 08 2022 08:45:55

%S 1,3,4,6,8,9,11,13,14,16,17,19,21,22,24,26,27,29,31,32,34,35,37,39,40,

%T 42,44,45,47,49,50,52,53,55,57,58,60,62,63,65,66,68,70,71,73,75,76,78,

%U 80,81,83,84,86,88,89,91,93,94,96,98,99,101,102,104

%N Beatty sequence for (5-sqrt(3))/2.

%C Let u=1+sqrt(3) and v=sqrt(3). Jointly rank {ju} and {kv} as in the first comment at A182760; a(n) is the position of nv. A182773 is the complement of A182771.

%H Vincenzo Librandi, <a href="/A182772/b182772.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(n*(5-sqrt(3))/2).

%o (Magma) [Floor(n*(5-Sqrt(3))/2): n in [1..80]]; // _Vincenzo Librandi_, Oct 25 2011

%Y Cf. A182760, A182771.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 30 2010