A189816 - OEIS

%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