|
%I #8 Sep 08 2022 08:45:57
%S 3,8,12,17,21,25,30,34,39,44,48,53,58,62,66,70,75,80,84,89,93,98,103,
%T 106,111,116,120,125,129,134,139,143,148,152,156,161,165,170,175,179,
%U 184,188,192,197,201,206,211,215,220,224,229,234,237,242,246,251,256,260,265,270,274,278,282,287,292,296,301,306,310,315,319,323
%N a(n) = n + [n*r/t] + [n*s/t] + [n*u/t]; r=sin(Pi/5), s=1/r, t=sin(2*Pi/5), u=1/t.
%C See A190372.
%H G. C. Greubel, <a href="/A190374/b190374.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].
%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/(2*cos(Pi/5))) + floor(n/(sin(Pi/5)*sin(2*Pi/5))) + floor(n/(sin(2*Pi/5)^2)), ", ")) \\ _G. C. Greubel_, Apr 05 2018
%o (Magma) R:=RealField(); [n + Floor(n/(2*Cos(Pi(R)/5))) + Floor(n/(Sin(Pi(R)/5)*Sin(2*Pi(R)/5))) + Floor(n/(Sin(2*Pi(R)/5)^2)): n in [1..100]]; // _G. C. Greubel_, Apr 05 2018
%Y Cf. A190372, A190373, A190375.
%K nonn
%O 1,1
%A _Clark Kimberling_, May 09 2011
|
