A054088 - OEIS

%I #25 Sep 08 2022 08:45:00

%S 2,5,8,10,13,16,19,21,24,27,30,32,35,38,40,43,46,49,51,54,57,60,62,65,

%T 68,71,73,76,79,81,84,87,90,92,95,98,101,103,106,109,112,114,117,120,

%U 122,125,128,131,133,136,139,142,144,147,150

%N a(n) = A054086(3n); also a bisection of A003511.

%F a(n) = floor( n*(1+sqrt(3)) ) = n + floor(n*sqrt(3)). - _R. J. Mathar_, Feb 26 2011

%F a(n) = n + A022838(n). - _R. J. Mathar_, Jan 25 2015

%F From _Miko Labalan_, Dec 17 2016: (Start)

%F For n > 0, a(n) = 3*floor(n*(sqrt(3)-1)) + 2*floor(n*(2-sqrt(3))) + 2;

%F a(0) = 0, a(n) = a(n - 1) + A022838(n) - A022838(n - 1) + 1. (End)

%p A054088 := proc(n) floor(n*(1+sqrt(3))) ; end proc: # _R. J. Mathar_, Feb 26 2011

%t Table[Floor[n (1 + Sqrt[3])], {n, 100}] (* _Wesley Ivan Hurt_, Dec 17 2016 *)

%o (Magma) [3*Floor(n*(Sqrt(3)-1))+2*Floor(n*(2-Sqrt(3)))+2: n in [1..60]]; // _Vincenzo Librandi_, Dec 18 2016

%Y Cf. A003511, A022838, A054086.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_

%E A-number in the definition corrected by _R. J. Mathar_, Oct 05 2008