A285518 {00->0, 11->1}-transform of A285504.

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

Offset

1

Comments

As a word, A285504 = 1111001100111111001100111111001100111111..., so that the substitutions 00-> and 11->1 leave 110101110101110101110101010101011101...

The sequence can also be given as the 1-limiting word of the morphism 0->11, 1->0101. The reason is that the generating morphism for A285504 is the morphism 0->11, 1-> 0011, which generates a 2-block morphism 00->11 11, 11->00 11 00 11. - Michel Dekking, Feb 28 2021

See A285519 and A285520 for conjectured connections to the golden ratio.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 0, 1, 1}}] &, {0}, 7] (* A285504 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"11" -> "1", "00" -> "0"}]
s1 = ToCharacterCode[w1] - 48 (* A285518 *)
Flatten[Position[s1, 0]]  (* A285519 *)
Flatten[Position[s1, 1]]  (* A285520  *)

Crossrefs

Cf. A285504, A285515, A285519, A285520.

Sequence in context: A103842 A286064 A065535 * A093719 A153778 A065251

Adjacent sequences: A285515 A285516 A285517 * A285519 A285520 A285521

Keyword

nonn,easy

Author

Clark Kimberling, Apr 30 2017

Status

approved