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

Author

Paul D. Hanna, Jan 22 2011

Keywords

• nonn

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.

Examples

			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...
		

Crossrefs

Cf. A184821, A184822, A184812, A058265; A184823, A184835.

Programs

PARI

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

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).