A190000 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sinh(1), t=cosh(1).

2, 5, 8, 12, 15, 18, 21, 24, 27, 31, 34, 37, 41, 43, 46, 50, 53, 56, 59, 63, 65, 68, 72, 75, 78, 82, 84, 87, 91, 94, 97, 101, 104, 106, 109, 113, 116, 119, 123, 126, 128, 132, 135, 138, 142, 145, 147, 151, 154, 157, 160, 164, 167, 169, 173, 176, 179, 183, 186, 189, 192, 195, 198, 202, 205, 208, 211, 214, 217, 220, 224, 227, 230, 233

Offset: 1

Author

Clark Kimberling, May 03 2011

Keywords

• nonn

Comments

See A189999.

Does the growth of a(n) oscillate with A020914(2*n-1), or does one sequence eventually outgrow the other? - Jeffrey R. Goodwin, Aug 26 2011

Links

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

Crossrefs

Cf. A189999, A190001.

Programs

Magma

[n + Floor(n/Sinh(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/sinh(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)].