A182777 - OEIS

%I #16 Sep 08 2022 08:45:55

%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 32,34,35,36,38,39,40,41,43,44,45,46,48,49,50,51,53,54,55,57,58,59,60,

%U 62,63,64,65,67,68,69,71,72,73,74,76,77,78,79,81,82,83,84,86

%N Beatty sequence for 3-sqrt(3).

%C (1) 3 is the only number x for which the numbers r=x-sqrt(x) and s=x+sqrt(x) satisfy the Beatty equation

%C 1/r + 1/s = 1.

%C (2) Let u=2-sqrt(3) and v=1.  Jointly rank {j*u} and {k*v} as in the first comment at A182760; a(n) is the position of n*u.

%C (3) The complement of A182777 is A182778, which gives the positions of the natural numbers k in the joint ranking.

%H Vincenzo Librandi, <a href="/A182777/b182777.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Table[Floor[(3-Sqrt[3]) n], {n, 68}]

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

%o (PARI) vector(80, n, floor(n*(3-sqrt(3)))) \\ _G. C. Greubel_, Nov 23 2018

%o (Sage) [floor(n*(3-sqrt(3))) for n in (1..80)] # _G. C. Greubel_, Nov 23 2018

%Y Cf. A182760, A182778.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 30 2010

%E Typo in formula by _Vincenzo Librandi_, Oct 25 2011