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A350127 a(n) = a(a(n-1)) mod 3 + a(n-2) with a(0) = 0 and a(1) = 1.

%I A350127 #15 Dec 19 2021 04:20:30
%S A350127 0,1,1,2,2,3,4,5,4,7,6,8,7,10,7,12,8,13,9,14,10,14,11,16,13,17,14,18,
%T A350127 14,19,16,21,18,21,20,22,22,24,23,25,25,27,25,29,26,31,26,33,26,35,27,
%U A350127 35,28,37,28,39,29,40,30,41,30,42,31,42,32,42,33,42,34
%N A350127 a(n) = a(a(n-1)) mod 3 + a(n-2) with a(0) = 0 and a(1) = 1.
%C A350127 It appears that lim_{n->infinity} a(n)/n = 0.562...
%C A350127 Are there infinitely many k such that a(k) = a(k+1)?
%C A350127 Conjecture: The density of even terms is 1/2.
%H A350127 Jon Maiga, <a href="/A350127/b350127.txt">Table of n, a(n) for n = 0..10000</a>
%t A350127 a[0] = 0;
%t A350127 a[1] = 1;
%t A350127 a[n_] := a[n] = Mod[a[a[n - 1]], 3] + a[n - 2]
%t A350127 Array[a, 100, 0]
%o A350127 (Python)
%o A350127 a = [0, 1]
%o A350127 [a.append(a[a[n-1]]%3 + a[n-2]) for n in range(2, 69)]
%o A350127 print(a) # _Michael S. Branicky_, Dec 15 2021
%Y A350127 Cf. A350126.
%K A350127 nonn,look
%O A350127 0,4
%A A350127 _Jon Maiga_, Dec 15 2021