A190327 a(n) = n + [n*r/s] + [n*t/s]; r=1/2, s=sinh(Pi/2), t=cosh(Pi/2).

2, 4, 6, 8, 11, 13, 15, 17, 19, 22, 24, 27, 29, 32, 34, 36, 38, 40, 43, 45, 47, 49, 52, 55, 57, 59, 61, 64, 66, 68, 70, 72, 75, 78, 80, 82, 85, 87, 89, 91, 93, 96, 98, 100, 103, 105, 108, 110, 112, 114, 117, 119, 121, 123, 125, 129, 131, 133, 135, 138, 140, 142, 144, 146, 149, 151, 154, 156, 158, 161, 163, 165, 167, 170

Offset

1,1

Comments

See A190326.

Links

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

Formula

A190326: f(n) = n + [2*n*sinh(Pi/2)] + [2*n*cosh(Pi/2)].

A190327: g(n) = n + [n*csch(Pi/2)/2] + [n*coth(Pi/2)].

A190328: h(n) = n + [n*sech(Pi/2)/2] + [n*tanh(Pi/2)].

Maple

r:=1/2: s:=sinh(Pi/2): t:=cosh(Pi/2): seq(n+floor(n*r/s)+floor(n*t/s), n=1..80); # Muniru A Asiru, Apr 05 2018

Mathematica

r=1/2; s=Sinh[Pi/2]; t=Cosh[Pi/2];
f[n_] := n + Floor[n*s/r] + Floor[n*t/r];
g[n_] := n + Floor[n*r/s] + Floor[n*t/s];
h[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[f[n], {n, 1, 120}]  (* A190326 *)
Table[g[n], {n, 1, 120}]  (* A190327 *)
Table[h[n], {n, 1, 120}]  (* A190328 *)

Prog

(PARI) for(n=1, 100, print1(n + floor(n/(2*sinh(Pi/2))) + floor(n/tanh(Pi/2)), ", ")) \\ G. C. Greubel, Apr 04 2018
(Magma) R:=RealField(); [n + Floor(n/(2*Sinh(Pi(R)/2))) + Floor(n/Tanh(Pi(R)/2)): n in [1..100]]; // G. C. Greubel, Apr 04 2018

Crossrefs

Cf. A190326, A190328.

Sequence in context: A287777 A249099 A329838 * A241176 A184809 A022839

Adjacent sequences: A190324 A190325 A190326 * A190328 A190329 A190330

Keyword

nonn

Author

Clark Kimberling, May 08 2011

Status

approved