A184820 a(n) = n + floor(n/t) + floor(n/t^2), where t is the tribonacci constant.

1, 3, 4, 7, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 28, 31, 32, 34, 35, 38, 39, 41, 44, 45, 47, 48, 51, 52, 54, 56, 58, 59, 62, 64, 65, 67, 69, 71, 72, 75, 76, 78, 80, 82, 84, 85, 88, 89, 91, 93, 95, 96, 98, 100, 102, 103, 106, 108, 109, 112, 113, 115, 116, 119, 120, 122, 124, 126, 128, 129, 132, 133, 135, 137, 139, 140, 143, 144, 146, 148, 150, 152, 153, 156, 157, 159, 161, 163, 164, 166, 169, 170, 172, 174, 176, 177, 179, 181, 183, 184, 187, 188, 190, 193, 194, 196, 197, 200, 201, 203, 205, 207, 208, 210, 213, 214, 216, 218, 220, 221, 224, 225, 227, 228, 231, 233, 234, 237, 238, 240, 242, 244, 245, 247

Offset

1,2

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..135.

Formula

Limit a(n)/n = t = 1.8392867552141611325518525646532866...

a(n) = n + floor(n*p/r) + floor(n*q/r), 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 = 1 + 1/t + 1/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. A184821, A184822, A184812, A058265; A184823, A184835.

Sequence in context: A286340 A024515 A187835 * A189521 A285346 A244736

Adjacent sequences: A184817 A184818 A184819 * A184821 A184822 A184823

Keyword

nonn

Author

Paul D. Hanna, Jan 22 2011

Status

approved