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%I #22 Sep 11 2022 00:50:38
%S 0,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,
%T 0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,
%U 0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,1,1
%N a(3*k-2)=0, a(3*k-1)=1-a(k), a(3*k)=1-a(k); k>0, a(1)=0.
%C Together with A189820, this sequence completes the list of "type 3,3" sequences described at A189628.
%C From _Michel Dekking_, Sep 09 2022: (Start)
%C For a complete list of "type 3,3" sequences, one still has to add 9 morphisms to the 15 morphisms in A189628 (two of which are given by A189816 and A189820).
%C Here is a list of these morphisms and their fixed points:
%C 0->001, 1->000: fixed point A182581
%C 0->001, 1->001: fixed point A022003
%C 0->001, 1->111: fixed point A189820
%C 0->010, 1->000: fixed point A356982
%C 0->010, 1->010: fixed point A022003 (n>0)
%C 0->010, 1->111: fixed point A319829
%C 0->011, 1->000: fixed point A189816 = (a(n))
%C 0->011, 1->011: fixed point A011655 (n->n+1)
%C 0->011, 1->111: fixed point A057427. (End)
%H G. C. Greubel, <a href="/A189816/b189816.txt">Table of n, a(n) for n = 1..10000</a>
%p A189816 := proc(n)
%p option remember;
%p if n = 1 then
%p 0;
%p else
%p if modp(n,3) = 1 then
%p 0 ;
%p else
%p 1-procname(ceil(n/3)) ;
%p end if ;
%p end if;
%p end proc:
%p seq(A189816(n),n=1..40) ; # _R. J. Mathar_, Jun 19 2021
%t Remove["Global`*"];
%t a[1] = 0; h = 180;
%t Table[a[3 k - 2] = 0, {k, 1, h}];
%t Table[a[3 k - 1] = 1 - a[k], {k, 1, h}];
%t Table[a[3 k] = 1 - a[k], {k, 1, h}];
%t Table[a[n], {n, 1, h}] (*A189816*)
%t Flatten[Position[%, 0]] (*A189817*)
%t Flatten[Position[%%, 1]] (*A189818*)
%Y Cf. A189628, A189817, A189818, A189819 (partial sums)
%K nonn
%O 1
%A _Clark Kimberling_, Apr 28 2011
%E Index in NAME corrected by _R. J. Mathar_, Jun 19 2021
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