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A190057 a(n) = n + [n*r/s] + [n*t/s];  r=1/2, s=sin(Pi/3), t=csc(Pi/3). 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 (list; graph; refs; listen; history; text; internal format)
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: A292643 A140101 A141207 * A190305 A294391 A257771

Adjacent sequences:  A190054 A190055 A190056 * A190058 A190059 A190060

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 04 2011

STATUS

approved

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Last modified November 28 16:42 EST 2021. Contains 349413 sequences. (Running on oeis4.)