A184733 a(n) = floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4; complement of A184732.

3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 44, 47, 50, 52, 55, 58, 60, 63, 65, 68, 71, 73, 76, 78, 81, 84, 86, 89, 92, 94, 97, 99, 102, 105, 107, 110, 112, 115, 118, 120, 123, 126, 128, 131, 133, 136, 139, 141, 144, 147, 149, 152, 154, 157, 160, 162, 165, 167, 170, 173, 175, 178, 181, 183, 186, 188, 191, 194, 196, 199, 201, 204, 207, 209, 212, 215, 217, 220, 222, 225, 228, 230, 233, 236, 238, 241, 243, 246, 249, 251, 254, 256, 259, 262, 264, 267, 270, 272, 275, 277, 280, 283, 285, 288, 291, 293, 296, 298, 301, 304, 306, 309, 311, 314

Offset: 1

Author

Clark Kimberling, Jan 20 2011

Keywords

• nonn

Links

• Jon Asier Bárcena-Petisco, Luis Martínez, María Merino, Juan Manuel Montoya, and Antonio Vera-López, Fibonacci-like partitions and their associated piecewise-defined permutations, arXiv:2503.19696 [math.CO], 2025. See p. 4.

Crossrefs

Cf. A184732, A184659.

Programs

Maple

A184733 := proc(n)
        phi := (1+sqrt(5))/2 ;
        n+floor((n+1/4)*phi) ;
end proc:
seq(A184733(n),n=1..100) ; # R. J. Mathar, Sep 04 2016

Mathematica

r=(1+sqrt(5))/2, h=-1/4; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184732 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (*A184733 *)

Formula

a(n) = floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4.