A184821 a(n) = n + floor(n*t) + floor(n/t), where t is the tribonacci constant.

2, 6, 9, 13, 16, 20, 22, 26, 29, 33, 36, 40, 43, 46, 50, 53, 57, 60, 63, 66, 70, 73, 77, 81, 83, 87, 90, 94, 97, 101, 104, 107, 110, 114, 118, 121, 125, 127, 131, 134, 138, 141, 145, 147, 151, 155, 158, 162, 165, 168, 171, 175, 178, 182, 185, 189, 191, 195, 199, 202, 206, 209, 212, 215, 219, 222, 226, 229, 232, 236, 239, 243, 246, 250, 252, 256, 259, 263, 266, 270, 273, 276, 280, 283, 287, 290, 294, 296, 300, 303, 307, 311, 314, 317, 320, 324, 327, 331, 334, 337, 340, 344, 347, 351, 355, 357, 361, 364, 368, 371, 375, 378, 381, 384, 388, 392, 395, 399, 401, 405, 408, 412, 415, 419, 421, 425, 429, 432

Offset

1,1

Comments

This is one of three sequences that partition the positive integers.

Given t is the tribonacci constant, then the following sequences are disjoint:

. A184820(n) = n + [n/t] + [n/t^2],

. A184821(n) = n + [n*t] + [n/t],

. A184822(n) = n + [n*t] + [n*t^2], where []=floor.

This is a special case of Clark Kimberling's results given in A184812.

Links

Table of n, a(n) for n=1..128.

Formula

Limit a(n)/n = t^2 = 3.3829757679...

a(n) = n + floor(n*p/q) + floor(n*r/q), where p=t, q=t^2, r=t^3, and t is the tribonacci constant (see Clark Kimberling's formula in A184812).

Example

Let t be the tribonacci constant, then t^2 = 1 + t + 1/t where:
t = 1.8392867552..., t^2 = 3.3829757679..., t^3 = 6.2222625231...

Prog

(PARI) {a(n)=local(t=real(polroots(1+x+x^2-x^3)[1])); n+floor(n*t)+floor(n/t)}

Crossrefs

Cf. A184820, A184822, A184812, A058265.

Sequence in context: A083789 A003145 A184621 * A292659 A184869 A047276

Adjacent sequences: A184818 A184819 A184820 * A184822 A184823 A184824

Keyword

nonn

Author

Paul D. Hanna, Jan 22 2011

Status

approved