A308186 Fixed point (beginning with a) of the morphism a -> abab, b -> b, over the alphabet {a,b} = {1,2}.

1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1

Offset

1,2

Comments

It seems likely that this is essentially 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, 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(1):= (1, 2, 1, 2):
f(2):= 2:
A:= [1]:
for i from 1 to 9 do A:= map(f, A) od:
A; # Robert Israel, Jun 05 2019

Mathematica

Nest[Flatten[ReplaceAll[#, 1->{1, 2, 1, 2}]]&, {1}, 6] (* Paolo Xausa, Nov 08 2023 *)

Crossrefs

Cf. A288932, A308185.

Sequence in context: A180227 A001468 A014675 * A107362 A166332 A378283

Adjacent sequences: A308183 A308184 A308185 * A308187 A308188 A308189

Keyword

nonn

Author

N. J. A. Sloane, Jun 05 2019

Status

approved