A190007 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sin(Pi/3), t=csc(Pi/3).

3, 6, 10, 13, 16, 20, 24, 27, 31, 34, 37, 41, 45, 48, 52, 55, 58, 62, 65, 69, 73, 76, 79, 83, 86, 90, 94, 97, 100, 104, 107, 110, 115, 118, 121, 125, 128, 131, 136, 139, 142, 146, 149, 152, 156, 160, 163, 167, 170, 173, 177, 181, 184, 188, 191, 194, 198, 201, 205, 209, 212, 215, 219, 222, 226, 230, 233, 236, 240, 243, 246, 251, 254

Offset: 1

Author

Clark Kimberling, May 03 2011

Keywords

• nonn
• easy

Comments

See A190006.

Links

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

Crossrefs

Cf. A190006, A190008.

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 *)

PARI

for(n=1,100, print1(n + floor(n/sin(Pi/3)) + floor(n/(sin(Pi/3))^2), ", ")) \\ G. C. Greubel, Jan 11 2018

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].