A190374 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.

3, 8, 12, 17, 21, 25, 30, 34, 39, 44, 48, 53, 58, 62, 66, 70, 75, 80, 84, 89, 93, 98, 103, 106, 111, 116, 120, 125, 129, 134, 139, 143, 148, 152, 156, 161, 165, 170, 175, 179, 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

Offset

1,1

Comments

See A190372.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

(* 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))].

(* 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))].

(* 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].

(* 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].

Mathematica

r=Sin[Pi/5]; s=1/r; t=Sin[2*Pi/5]; u=1/t;
f[n_] := n + Floor[n*s/r] + Floor[n*t/r] + Floor[n*u/r];
g[n_] := n + Floor[n*r/s] + Floor[n*t/s] + Floor[n*u/s];
h[n_] := n + Floor[n*r/t] + Floor[n*s/t] + Floor[n*u/t];
i[n_] := n + Floor[n*r/u] + Floor[n*s/u] + Floor[n*t/u];
Table[f[n], {n, 1, 120}]  (* A190372 *)
Table[g[n], {n, 1, 120}]  (* A190373 *)
Table[h[n], {n, 1, 120}]  (* A190374 *)
Table[i[n], {n, 1, 120}]  (* A190375 *)

Prog

(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
(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

Crossrefs

Cf. A190372, A190373, A190375.

Sequence in context: A022806 A084162 A140103 * A189758 A190368 A256711

Adjacent sequences: A190371 A190372 A190373 * A190375 A190376 A190377

Keyword

nonn

Author

Clark Kimberling, May 09 2011

Status

approved