A285515 {00->0, 11->1}-transform of A285501.

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, 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

Offset

1

Comments

As a word, A285501 = 0011001100110011111100110011111100110011..., so that the transform of A285501 that results from the substitutions 00-> and 11->1 is 01010101110101110101010101011101011101010... The sequence is also the 0-limiting word of the morphism 0->11, 1->0101. See A285517 and A285518 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}, 6] (* A285501 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"00" -> "0", "11" -> "1"}]
s1 = ToCharacterCode[w1] - 48 (* A285515 *)
Flatten[Position[s1, 0]]  (* A285516 *)
Flatten[Position[s1, 1]]  (* A285517  *)

Crossrefs

Cf. A285501, A285516, A285517, A285518, A285589.

Sequence in context: A189219 A189008 A353681 * A190204 A189028 A301850

Adjacent sequences: A285512 A285513 A285514 * A285516 A285517 A285518

Keyword

nonn,easy

Author

Clark Kimberling, Apr 30 2017

Status

approved