A189816 a(3*k-2)=0, a(3*k-1)=1-a(k), a(3*k)=1-a(k); k>0, a(1)=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, 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

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A189813 A189814 A189815 * A189817 A189818 A189819

Keyword

nonn

Author

Clark Kimberling, Apr 28 2011

Extensions

Index in NAME corrected by R. J. Mathar, Jun 19 2021

Status

approved