A189927 b(n) = n + [n*r/s] + [n*t/s]; r=1, s=sin(Pi/5), t=cos(Pi/5), where [] denotes the floor function.

3, 7, 12, 15, 19, 24, 27, 32, 36, 40, 44, 48, 52, 56, 60, 65, 68, 72, 77, 81, 84, 89, 93, 97, 101, 105, 109, 113, 117, 122, 125, 130, 134, 137, 142, 146, 149, 154, 158, 163, 166, 170, 175, 178, 182, 187, 190, 195, 199, 203, 207, 211, 215, 219, 223, 228

Offset

1,1

Links

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

Formula

A189926: a(n) = n + [n*sin(pi/5)] + [n*cos(Pi/5)].

A189927: b(n) = n + [n*csc(pi/5)] + [n*cot(Pi/5)].

A189928: c(n) = n + [n*sec(pi/5)] + [n*tan(Pi/5)].

Mathematica

r=1; s=Sin[Pi/5]; t=Cos[Pi/5];
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}]  (* A189926 *)
Table[b[n], {n, 1, 120}]  (* A189927 *)
Table[c[n], {n, 1, 120}]  (* A189928 *)

Prog

(PARI) for(n=1, 100, print1(n + floor(n/sin(Pi/5)) + floor(n/tan(Pi/5)), ", ")) \\ G. C. Greubel, Jan 13 2018
(Magma) C<i> := ComplexField(); [n + Floor(n/Sin(Pi(C)/5)) + Floor(n/Tan(Pi(C)/5)): n in [1..100]]; // G. C. Greubel, Jan 13 2018

Crossrefs

Cf. A189926, A189928.

Sequence in context: A310228 A310229 A083031 * A189403 A022805 A310230

Adjacent sequences: A189924 A189925 A189926 * A189928 A189929 A189930

Keyword

nonn

Author

Clark Kimberling, May 01 2011

Status

approved