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

%I A184733 #11 Mar 30 2025 11:23:34
%S A184733 3,5,8,10,13,16,18,21,23,26,29,31,34,37,39,42,44,47,50,52,55,58,60,63,
%T A184733 65,68,71,73,76,78,81,84,86,89,92,94,97,99,102,105,107,110,112,115,
%U A184733 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
%N A184733 a(n) = floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4; complement of A184732.
%H A184733 Jon Asier Bárcena-Petisco, Luis Martínez, María Merino, Juan Manuel Montoya, and Antonio Vera-López, <a href="https://arxiv.org/abs/2503.19696">Fibonacci-like partitions and their associated piecewise-defined permutations</a>, arXiv:2503.19696 [math.CO], 2025. See p. 4.
%F A184733 a(n) = floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4.
%p A184733 A184733 := proc(n)
%p A184733         phi := (1+sqrt(5))/2 ;
%p A184733         n+floor((n+1/4)*phi) ;
%p A184733 end proc:
%p A184733 seq(A184733(n),n=1..100) ; # _R. J. Mathar_, Sep 04 2016
%t A184733 r=(1+sqrt(5))/2, h=-1/4; s=r/(r-1);
%t A184733 Table[Floor[n*r+h],{n,1,120}]  (* A184732 *)
%t A184733 Table[Floor[n*s+h-h*s],{n,1,120}]  (*A184733 *)
%Y A184733 Cf. A184732, A184659.
%K A184733 nonn
%O A184733 1,1
%A A184733 _Clark Kimberling_, Jan 20 2011