A190003 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=(sinh(1))^2, t=(cosh(1))^2.

2, 6, 10, 12, 16, 20, 24, 26, 30, 34, 36, 40, 44, 48, 50, 54, 58, 62, 64, 68, 72, 74, 78, 82, 86, 88, 92, 96, 98, 102, 106, 110, 112, 116, 120, 124, 126, 130, 134, 136, 140, 144, 148, 150, 154, 158, 162, 164, 168, 172, 174, 178, 182, 186, 188, 192, 196, 198, 202, 206, 210, 212, 216, 220, 224, 226, 230, 234, 236, 240

Offset: 1

Author

Clark Kimberling, May 03 2011

Keywords

• nonn

Comments

See A190002.

Links

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

Crossrefs

Cf. A190002, A182760.

Programs

Magma

[n + Floor(n/(Sinh(1))^2) + Floor(n/(Tanh(1))^2): n in [1..100]]; // G. C. Greubel, Jan 11 2018

Maple

seq(n+floor(n/s)+floor(n*t/s), n=1..100); # Robert Israel, Jan 12 2018

Mathematica

r=1; s=Sinh[1]^2; t=Cosh[1]^2;
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}]  (* A190002 *)
Table[b[n], {n, 1, 120}]  (* A190003 *)
Table[c[n], {n, 1, 120}]  (* A005408 *)
Table[a[n]/2, {n, 1, 120}](* A190004 *)
Table[b[n]/2, {n, 1, 120}](* A182760 *)

PARI

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

Formula

A190002: a(n) = n + [n*(sinh(1))^2] + [n*(cosh(1))^2].

A190003: b(n) = n + [n*(csch(1))^2] + [n*(coth(1))^2].

A005408: c(n) = 2*n - 1.