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A214988 Beatty sequence for sqrt(r), where r = (1+sqrt(5))/2 = golden ratio; complement of A214989. 2

%I #6 Nov 13 2012 13:01:33

%S 1,2,3,5,6,7,8,10,11,12,13,15,16,17,19,20,21,22,24,25,26,27,29,30,31,

%T 33,34,35,36,38,39,40,41,43,44,45,47,48,49,50,52,53,54,55,57,58,59,61,

%U 62,63,64,66,67,68,69,71,72,73,75,76,77,78,80,81,82,83,85,86

%N Beatty sequence for sqrt(r), where r = (1+sqrt(5))/2 = golden ratio; complement of A214989.

%H Clark Kimberling, <a href="/A214988/b214988.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(t*n), where t=sqrt((1+sqrt(5))/2).

%e a(1) = floor(t) = 1, a(2) = floor(2*t) = 2, where t=sqrt((1+sqrt(5))/2).

%t r = Sqrt[GoldenRatio]; s = r/(r - 1);

%t Table[Floor[r*n], {n, 1, 120}] (* A214988 *)

%t Table[Floor[s*n], {n, 1, 120}] (* A214989 *)

%Y Cf. A214989.

%K nonn

%O 1,2

%A _Clark Kimberling_, Oct 28 2012

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Last modified August 28 06:46 EDT 2024. Contains 375477 sequences. (Running on oeis4.)