A285677 {0010->2}-transform of the infinite Fibonacci word A003849.

0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2

Offset: 1

Author

Clark Kimberling, May 11 2017

Keywords

• nonn
• easy

Comments

As a word, A003849 = 01001010010010100..., and replacing each 0010 by 2 gives 0121201012120101201012120101212010...

Warning: "replacing each 0010 by 2" means "replacing each 0010 by 2 from left to right, consecutively". The result is that the word a(8)...a(14)=0010010 in A003849 is replaced by 201, not by 22. - Michel Dekking, Aug 27 2018

Links

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

Crossrefs

Cf. A003849, A284620, A285678, A182761, A285679.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0010" -> "2"}]
st = ToCharacterCode[w1] - 48; (* A285677 *)
Flatten[Position[st, 0]];  (* A285678 *)
Flatten[Position[st, 1]];  (* A182761 - conjectured *)
Flatten[Position[st, 2]];  (* A285679 *)