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A189816
a(3*k-2)=0, a(3*k-1)=1-a(k), a(3*k)=1-a(k); k>0, a(1)=0.
6
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, 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, 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
OFFSET
1
COMMENTS
Together with A189820, this sequence completes the list of "type 3,3" sequences described at A189628.
From Michel Dekking, Sep 09 2022: (Start)
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).
Here is a list of these morphisms and their fixed points:
0->001, 1->000: fixed point A182581
0->001, 1->001: fixed point A022003
0->001, 1->111: fixed point A189820
0->010, 1->000: fixed point A356982
0->010, 1->010: fixed point A022003 (n>0)
0->010, 1->111: fixed point A319829
0->011, 1->000: fixed point A189816 = (a(n))
0->011, 1->011: fixed point A011655 (n->n+1)
0->011, 1->111: fixed point A057427. (End)
LINKS
MAPLE
A189816 := proc(n)
option remember;
if n = 1 then
0;
else
if modp(n, 3) = 1 then
0 ;
else
1-procname(ceil(n/3)) ;
end if ;
end if;
end proc:
seq(A189816(n), n=1..40) ; # R. J. Mathar, Jun 19 2021
MATHEMATICA
Remove["Global`*"];
a[1] = 0; h = 180;
Table[a[3 k - 2] = 0, {k, 1, h}];
Table[a[3 k - 1] = 1 - a[k], {k, 1, h}];
Table[a[3 k] = 1 - a[k], {k, 1, h}];
Table[a[n], {n, 1, h}] (*A189816*)
Flatten[Position[%, 0]] (*A189817*)
Flatten[Position[%%, 1]] (*A189818*)
CROSSREFS
Cf. A189628, A189817, A189818, A189819 (partial sums)
Sequence in context: A072608 A295304 A171386 * A342000 A194685 A182582
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 28 2011
EXTENSIONS
Index in NAME corrected by R. J. Mathar, Jun 19 2021
STATUS
approved