%I #18 Sep 12 2020 03:28:51
%S 1,4,7,9,12,15,16,19,20,23,26,28,31,34,35,37,40,43,44,46,49,52,53,56,
%T 59,61,64,66,69,72,73,76,79,81,82,85,86,89,92,94,97,100,101,103,106,
%U 108,111,114,115,118,121,123,124,127,130,132,135,138,139,142
%N a(1)=1, a(n)=a(n-1)+1 if n is odd and already in the sequence, a(n)=a(n-1)+2 if n is even and already in the sequence, a(n)=a(n-1)+3 otherwise.
%H Amiram Eldar, <a href="/A080574/b080574.txt">Table of n, a(n) for n = 1..10000</a>
%H Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%F It appears that a(n) is asymptotic to c*n where c=2.36... is the largest root of q^2-3*q+3/2 = 0.
%t a[1] = 1;
%t a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], If[OddQ[n], a[n-1]+1, a[n-1]+2], a[n-1]+3];
%t Array[a, 60] (* _Jean-François Alcover_, Feb 13 2019 *)
%K nonn
%O 1,2
%A _Benoit Cloitre_, Mar 23 2003