A190057 - OEIS

%I #13 Sep 08 2022 08:45:56

%S 2,5,8,11,13,17,20,22,26,28,31,34,37,40,43,46,48,52,54,57,61,63,66,69,

%T 72,75,78,81,83,87,89,92,96,98,101,104,107,109,113,116,118,122,124,

%U 127,130,133,136,139,142,144,148,151,153,157,159,162,165,168,171,174,177,179,183,185,188,192,194,197,200,203,205,209,212,214

%N a(n) = n + [n*r/s] + [n*t/s];  r=1/2, s=sin(Pi/3), t=csc(Pi/3).

%C See A190056.

%H G. C. Greubel, <a href="/A190057/b190057.txt">Table of n, a(n) for n = 1..10000</a>

%F A190056:  a(n) = n + [2*n*sin(Pi/3)] + [2*n*csc(Pi/3)].

%F A190057:  b(n) = n + [(n/2)*csc(Pi/3)] + [n*(csc(Pi/3))^2].

%F A190058:  c(n) = n + [(n/2)*sin(Pi/3)] + [n*(sin(Pi/3))^2].

%t r=1/2; s=Sin[Pi/3]; t=Csc[Pi/3];

%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[a[n], {n, 1, 120}]  (* A190056 *)

%t Table[b[n], {n, 1, 120}]  (* A190057 *)

%t Table[c[n], {n, 1, 120}]  (* A190058 *)

%o (PARI) for(n=1,70, print1(n + floor(n/(2*sin(Pi/3))) + floor(n/(sin(Pi/3))^2), ", ")) \\ _G. C. Greubel_, Jan 10 2018

%o (Magma) C<i> := ComplexField(); [n + Floor(n/(2*Sin(Pi(C)/3))) + Floor(n/(Sin(Pi(C)/3))^2): n in [1..70]]; // _G. C. Greubel_, Jan 10 2018

%Y Cf. A190056, A190058.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 04 2011