A190370 a(n) = n + [n*r/t] + [n*s/t] + [n*u/t]; r=sin(Pi/5), s=cos(Pi/5), t=sin(2*Pi/5), u=cos(2*Pi/5).

1, 4, 6, 10, 13, 15, 18, 20, 23, 27, 29, 32, 36, 37, 40, 43, 46, 49, 52, 55, 56, 60, 63, 65, 69, 72, 73, 77, 79, 82, 86, 88, 91, 94, 96, 99, 102, 105, 108, 110, 113, 115, 118, 122, 124, 127, 130, 132, 135, 138, 141, 144, 147, 149, 151, 155, 158, 160, 164, 167, 168, 172, 174, 177, 181, 183, 185, 189, 191, 194, 197, 200

Offset

1,2

Comments

See A190368.

Links

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

Formula

A190368: f(n) = n + floor(n*cot(Pi/5)) + floor(2*n*cos(Pi/5)] + floor(n*cos(2*Pi/5)/sin(Pi/5)).

A190369: g(n) = n + floor(n*tan(Pi/5)) + floor(2*n*sin(Pi/5)] + floor(n*cos(2*Pi/5)/cos(Pi/5)).

A190370: h(n) = n + floor(n*sec(Pi/5)/2) + floor(n*csc(Pi/5)/2] + floor(n*cot(2*Pi/5)).

A190371: i(n) = n + floor(n*sin(Pi/5)/cos(2*Pi/5)) + floor(n*cos(Pi/5)/cos(2*Pi/5)) + floor(n*tan(2*Pi/5)).

Maple

r:=sin(Pi/5): s:=cos(Pi/5): t:=sin(2*Pi/5): u:=cos(2*Pi/5): seq(n+floor(n*r/t)+floor(n*s/t)+floor(n*u/t), n=1..80); # Muniru A Asiru, Apr 08 2018

Mathematica

r=Sin[Pi/5]; s=Cos[Pi/5]; t=Sin[2*Pi/5]; u=Cos[2*Pi/5];
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}]  (* A190368 *)
Table[g[n], {n, 1, 120}]  (* A190369 *)
Table[h[n], {n, 1, 120}]  (* A190370 *)
Table[i[n], {n, 1, 120}]  (* A190371 *)

Prog

(PARI) for(n=1, 100, print1(n + floor(n/(2*cos(Pi/5))) + floor(n/(2*sin(Pi/5))) + floor(n/tan(2*Pi/5)), ", ")) \\ G. C. Greubel, Apr 05 2018
(Magma) R:=RealField(); [n + Floor(n/(2*Cos(Pi(R)/5))) + Floor(n/(2*Sin(Pi(R)/5))) + Floor(n/Tan(2*Pi(R)/5)): n in [1..100]]; // G. C. Greubel, Apr 05 2018

Crossrefs

Cf. A190368, A190369, A190371.

Sequence in context: A234965 A320881 A224796 * A246439 A186514 A184402

Adjacent sequences: A190367 A190368 A190369 * A190371 A190372 A190373

Keyword

nonn

Author

Clark Kimberling, May 09 2011

Status

approved