%I #15 Sep 08 2022 08:45:57
%S 1,4,6,9,11,14,16,18,22,24,26,29,32,33,37,38,41,45,46,49,51,54,56,59,
%T 61,64,67,69,72,74,77,79,82,85,87,90,91,95,97,99,102,104,107,110,112,
%U 114,118,119,122,124,127,130,132,135,137,140,142,145,147,150,153,155,157,160,163,164,168,171,172,176,177,180,183,185,187,190
%N a(n) = n + floor(n*r/s) + floor(n*t/s) + floor(n*u/s), where r = sin(Pi/5), s = 1/r, t = sin(2*Pi/5), u = 1/t.
%C See A190372.
%H G. C. Greubel, <a href="/A190373/b190373.txt">Table of n, a(n) for n = 1..10000</a>
%F (* A190372 *) f[n_] := n + Floor[n/sin(Pi/5)^2] + Floor[2*n*cos(Pi/5)] + Floor[n/(sin(2*Pi/5)*sin(Pi/5))].
%F (* A190373 *) g[n_] := n + Floor[n*sin(Pi/5)^2] + Floor[n*sin(Pi/5)* sin(2*Pi/5)] + Floor[n/(2*cos(Pi/5))].
%F (* A190374 *) h[n_] := n + Floor[n/(2*cos(Pi/5))] + Floor[n/(sin(Pi/5)* sin(2*Pi/5))] + Floor[n/sin(2*Pi/5)^2].
%F (* A190375 *) i[n_] := n + Floor[n*sin(Pi/5)*sin(2*Pi/5)] + Floor[2*n*cos(Pi/5)] + Floor[n*sin(2*Pi/5)^2].
%p A190373:=n->n+floor(n*sin(Pi/5)^2)+floor(n*sin(2*Pi/5)*sin(Pi/5))+floor(n*sin(Pi/5)/sin(2*Pi/5)): seq(A190373(n), n=1..100); # _Wesley Ivan Hurt_, Jan 31 2017
%t r=Sin[Pi/5]; s=1/r; t=Sin[2*Pi/5]; u=1/t;
%t f[n_] := n + Floor[n*s/r] + Floor[n*t/r] + Floor[n*u/r];
%t g[n_] := n + Floor[n*r/s] + Floor[n*t/s] + Floor[n*u/s];
%t h[n_] := n + Floor[n*r/t] + Floor[n*s/t] + Floor[n*u/t];
%t i[n_] := n + Floor[n*r/u] + Floor[n*s/u] + Floor[n*t/u];
%t Table[f[n], {n, 1, 120}] (* A190372 *)
%t Table[g[n], {n, 1, 120}] (* A190373 *)
%t Table[h[n], {n, 1, 120}] (* A190374 *)
%t Table[i[n], {n, 1, 120}] (* A190375 *)
%o (PARI) for(n=1,100, print1(n + floor(n*sin(Pi/5)^2) + floor(n*sin(Pi/5)*sin(2*Pi/5)) + floor(n/(2*cos(Pi/5))), ", ")) \\ _G. C. Greubel_, Apr 05 2018
%o (Magma) R:=RealField(); [n + Floor(n*Sin(Pi(R)/5)^2) + Floor(n*Sin(Pi(R)/5)*Sin(2*Pi(R)/5)) + Floor(n/(2*Cos(Pi(R)/5))): n in [1..100]]; // _G. C. Greubel_, Apr 05 2018
%Y Cf. A190372, A190374, A190375.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, May 09 2011