A308187 Fixed point (beginning with a) of the morphism a -> aab, b -> b, over the alphabet {a,b} = {0,1}.

0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0

Offset

1

Comments

Conjecture: characteristic function of A055938. - Sean A. Irvine, Jul 16 2022

Links

Rémy Sigrist, Table of n, a(n) for n = 1..16383

M. Bucci, A. De Luca, A. Glen and L. Q. Zamboni, A connection between palindromic and factor complexity using return words, arXiv:0802.1332 [math.CO], 2008. See Section 4.

Formula

a(0) = a(1) = 0, a(2) = 1; for n > 2, a(n) = 1 iff reducing n modulo A092323(n), ..., 7, 3 in turn yields 0. - Charlie Neder, Jun 10 2019

Example

From Charlie Neder, Jun 10 2019: (Start)
a(100000) = 1 because
   100000 = 34465 modulo 65535,
    34465 =  1698 modulo 32767,
     1698 =   675 modulo  1023,
      675 =   164 modulo   511,
      164 =    37 modulo   127,
       31 =     6 modulo    31, and
        6 =     0 modulo     3. (End)

Mathematica

Nest[Flatten[ReplaceAll[#, 0->{0, 0, 1}]]&, {0}, 6] (* Paolo Xausa, Nov 08 2023 *)

Crossrefs

Cf. A079559 (as 1,0), A308188 (as 1,2).

Cf. A308185, A308186.

Sequence in context: A189624 A014707 A288213 * A289007 A308901 A286804

Adjacent sequences: A308184 A308185 A308186 * A308188 A308189 A308190

Keyword

nonn

Author

N. J. A. Sloane, Jun 05 2019

Extensions

More terms from Rémy Sigrist, Jul 08 2019

Status

approved