A184822 a(n) = n + floor(n*t) + floor(n*t^2), where t is the tribonacci constant.

5, 11, 18, 24, 30, 37, 42, 49, 55, 61, 68, 74, 79, 86, 92, 99, 105, 111, 117, 123, 130, 136, 142, 149, 154, 160, 167, 173, 180, 186, 192, 198, 204, 211, 217, 223, 230, 235, 241, 248, 254, 261, 267, 272, 279, 285, 291, 298, 304, 310, 316, 322, 329, 335, 342, 348, 353, 360, 366, 372, 379, 385, 391, 397, 403, 410, 416, 423, 428, 434, 441, 447, 453, 460, 465, 472, 478, 484, 491, 497, 503, 509, 515, 522, 528, 534, 541, 546, 553, 559, 565, 572, 578, 583, 590, 596, 603, 609, 615, 621, 627, 634, 640, 646, 653, 658, 664, 671, 677, 684, 690, 696, 702, 708, 715, 721, 727, 734, 739, 745, 752, 758, 765, 771

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..124.

Formula

Limit a(n)/n = t^3 = 6.2222625231...

a(n) = n + floor(n*q/p) + floor(n*r/p), 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^3 = 1 + t + t^2 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^2)}

Crossrefs

Cf. A184820, A184821, A184812, A058265.

Sequence in context: A314270 A314271 A314272 * A145005 A004083 A190365

Adjacent sequences: A184819 A184820 A184821 * A184823 A184824 A184825

Keyword

nonn

Author

Paul D. Hanna, Jan 22 2011

Status

approved