A190001 a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sinh(1), t=cosh(1).

1, 4, 6, 9, 11, 13, 16, 19, 20, 23, 26, 28, 30, 33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 57, 60, 61, 64, 67, 69, 71, 74, 76, 79, 81, 83, 86, 88, 90, 93, 95, 98, 100, 102, 105, 108, 110, 112, 115, 117, 120, 122, 124, 127, 129, 131, 134, 136, 139, 141, 143, 146, 149, 150, 153, 156, 158, 161, 163, 165, 168, 171, 172, 175, 177, 180

Offset: 1

Author

Clark Kimberling, May 03 2011

Keywords

• nonn
• easy

Comments

See A189999.

Links

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

Crossrefs

Cf. A189999, A190000.

Programs

Magma

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

Mathematica

r=1; s=Sinh[1]; t=Cosh[1];
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}]  (* A189999 *)
Table[b[n], {n, 1, 120}]  (* A190000 *)
Table[c[n], {n, 1, 120}]  (* A190001 *)

PARI

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

Formula

A189999: a(n) = n + [n*sinh(1)] + [n*cosh(1)].

A190000: b(n) = n + [n*csch(1)] + [n*coth(1)].

A190001: c(n) = n + [n*sech(1)] + [n*tanh(1)].