A190008 a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sin(Pi/3), t=csc(Pi/3).

1, 4, 7, 10, 12, 15, 18, 20, 22, 25, 28, 31, 33, 36, 38, 41, 43, 46, 49, 52, 54, 57, 59, 62, 64, 67, 70, 73, 75, 77, 80, 83, 85, 88, 91, 94, 96, 98, 101, 104, 106, 109, 112, 115, 116, 119, 122, 125, 127, 130, 133, 136, 137, 140, 143, 146, 148, 151, 154, 156, 158, 161, 164, 167, 169, 172, 175, 177, 179, 182, 185, 188, 190

Offset: 1

Author

Clark Kimberling, May 03 2011

Keywords

• nonn

Comments

See A190006.

Links

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

Crossrefs

Cf. A190006, A190007.

Programs

Magma

C := ComplexField(); [n + Floor(n*Sin(Pi(C)/3)) + Floor(n*(Sin(Pi(C)/3))^2): n in [1..100]]; // G. C. Greubel, Jan 11 2018

Mathematica

r=1; 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}]  (* A190006 *)
Table[b[n], {n, 1, 120}]  (* A190007 *)
Table[c[n], {n, 1, 120}]  (* A190008 *)

Formula

A190006: a(n) = n + [n*sin(Pi/3)] + [n*csc(Pi/3)].

A190007: b(n) = n + [n*csc(Pi/3)] + [n*(csc(Pi/3))^2].

A190008: c(n) = n + [n*sin(Pi/3)] + [n*(sin(Pi/3))^2].