A190057 a(n) = n + [n*r/s] + [n*t/s]; r=1/2, s=sin(Pi/3), t=csc(Pi/3).

2, 5, 8, 11, 13, 17, 20, 22, 26, 28, 31, 34, 37, 40, 43, 46, 48, 52, 54, 57, 61, 63, 66, 69, 72, 75, 78, 81, 83, 87, 89, 92, 96, 98, 101, 104, 107, 109, 113, 116, 118, 122, 124, 127, 130, 133, 136, 139, 142, 144, 148, 151, 153, 157, 159, 162, 165, 168, 171, 174, 177, 179, 183, 185, 188, 192, 194, 197, 200, 203, 205, 209, 212, 214

Offset

1,1

Comments

See A190056.

Links

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

Formula

A190056: a(n) = n + [2*n*sin(Pi/3)] + [2*n*csc(Pi/3)].

A190057: b(n) = n + [(n/2)*csc(Pi/3)] + [n*(csc(Pi/3))^2].

A190058: c(n) = n + [(n/2)*sin(Pi/3)] + [n*(sin(Pi/3))^2].

Mathematica

r=1/2; s=Sin[Pi/3]; t=Csc[Pi/3];
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 120}]  (* A190056 *)
Table[b[n], {n, 1, 120}]  (* A190057 *)
Table[c[n], {n, 1, 120}]  (* A190058 *)

Prog

(PARI) for(n=1, 70, print1(n + floor(n/(2*sin(Pi/3))) + floor(n/(sin(Pi/3))^2), ", ")) \\ G. C. Greubel, Jan 10 2018
(Magma) C<i> := ComplexField(); [n + Floor(n/(2*Sin(Pi(C)/3))) + Floor(n/(Sin(Pi(C)/3))^2): n in [1..70]]; // G. C. Greubel, Jan 10 2018

Crossrefs

Cf. A190056, A190058.

Sequence in context: A376954 A140101 A141207 * A190305 A294391 A257771

Adjacent sequences: A190054 A190055 A190056 * A190058 A190059 A190060

Keyword

nonn

Author

Clark Kimberling, May 04 2011

Status

approved