A190375 - OEIS

%I #8 Sep 08 2022 08:45:57

%S 2,7,10,15,19,23,27,31,36,40,43,47,52,55,60,63,68,73,76,81,83,88,92,

%T 96,100,105,109,113,117,121,126,128,133,138,141,146,149,154,158,162,

%U 166,169,174,178,182,186,191,194,199,202,207,212,214,219,222,227,231,235,239,244,248,252,255,259,264,267,272,277,280,285,288,293,297,300

%N a(n) = n + [n*r/u] + [n*s/u] + [n*t/u];  r=sin(Pi/5), s=1/r, t=sin(2*Pi/5), u=1/t.

%C See A190372.

%H G. C. Greubel, <a href="/A190375/b190375.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*sin(Pi/5)*sin(2*Pi/5)) + floor(2*n*cos(Pi/5)) + floor(n*sin(2*Pi/5)^2), ", ")) \\ _G. C. Greubel_, Apr 05 2018

%o (Magma) R:=RealField(); [n + Floor(n*Sin(Pi(R)/5)*Sin(2*Pi(R)/5)) + Floor(2*n*Cos(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, A190374.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 09 2011