A285518 - OEIS

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

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OFFSET

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.