A190058 a(n) = n + [n*r/t] + [n*s/t]; r=1/2, s=sin(Pi/3), t=csc(Pi/3).

1, 3, 6, 8, 10, 12, 15, 17, 18, 21, 23, 26, 27, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 52, 53, 56, 58, 61, 62, 64, 67, 69, 71, 73, 76, 78, 80, 82, 84, 87, 88, 91, 93, 96, 97, 99, 102, 104, 106, 108, 111, 113, 114, 117, 119, 122, 123, 126, 128, 130, 132, 134, 137, 139, 141, 143, 146, 148, 149, 152, 154, 157, 158, 161, 163, 165, 167

Offset

1,2

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, 30, print1(n + floor(n*sin(Pi/3)/2) + floor(n*(sin(Pi/3))^2), ", ")) \\ G. C. Greubel, Jan 10 2018
(Magma) C<i> := ComplexField(); [n + Floor(n*Sin(Pi(C)/3)/2) + Floor(n*(Sin(Pi(C)/3))^2): n in [1..30]]; // G. C. Greubel, Jan 10 2018

Crossrefs

Cf. A190056, A190057.

Sequence in context: A112234 A189467 A023983 * A159061 A257874 A180398

Adjacent sequences: A190055 A190056 A190057 * A190059 A190060 A190061

Keyword

nonn

Author

Clark Kimberling, May 04 2011

Status

approved