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A285518
{00->0, 11->1}-transform of A285504.
8
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 30 2017
STATUS
approved