A308185 Fixed point (beginning with a) of the morphism a -> abab, b -> b, over the alphabet {a,b} = {0,1}.

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

Offset

1

Comments

It seems likely that this is the same sequence as A288932 without its leading 0, but the two definitions are so different that it is worth having both versions.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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.

A. Glen, J. Justin, S. Widmer, L. Q. Zamboni, Palindromic richness, arXiv:0801.1656 [math.CO], 2008.

Maple

f:= 'f':
f(0):= (0, 1, 0, 1):
f(1):= 1:
A:= [0]:
for i from 1 to 9 do A:= map(f, A) od:
A; # Robert Israel, Jun 05 2019

Mathematica

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

Crossrefs

Cf. A288932, A308186.

Sequence in context: A286665 A096270 A334820 * A159689 A174282 A189301

Adjacent sequences: A308182 A308183 A308184 * A308186 A308187 A308188

Keyword

nonn

Author

N. J. A. Sloane, Jun 05 2019

Status

approved