A190373 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.

1, 4, 6, 9, 11, 14, 16, 18, 22, 24, 26, 29, 32, 33, 37, 38, 41, 45, 46, 49, 51, 54, 56, 59, 61, 64, 67, 69, 72, 74, 77, 79, 82, 85, 87, 90, 91, 95, 97, 99, 102, 104, 107, 110, 112, 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

Offset

1,2

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].

Maple

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

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*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
(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

Crossrefs

Cf. A190372, A190374, A190375.

Sequence in context: A186318 A186345 A285976 * A329784 A010387 A010411

Adjacent sequences: A190370 A190371 A190372 * A190374 A190375 A190376

Keyword

nonn,easy

Author

Clark Kimberling, May 09 2011

Status

approved