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A284893 Fixed point of the morphism 0 -> 01, 1 -> 0111. 5
0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

From Michel Dekking, Jan 23 2018: (Start)

The four sequences A285373, A284939, A284893 and A285341 together form a conjugacy class of morphisms, where two morphisms are conjugated if one can obtain one from the other by a rotation R. Here the R-operator which maps certain morphisms sigma on {0,1} to a morphism R[sigma] is defined as follows.

If sigma(0)=c(1)c(2)...c(m), sigma(1)=d(1)d(2)…d(n), then R[sigma](0)=c(2)…c(m)c(1), R[sigma](1)=d(2)…d(n)d(1) (only if c(1)=d(1)).

With exception of some special cases, a conjugacy class of cardinality L forms a chain of morphisms (alpha, R[alpha], ..., R^{L-1}[alpha]), where the last morphism (or its square) has two fixed points, and the others have just one fixed point.

It is well known and easy to prove that two conjugated morphisms generate the same language. This implies that automatic cross-referencing occurs:  if one looks up a sequence b occurring in one of A285373, A284939, A284893 or A285341, then also the other 3 will turn up in the OEIS list. However, this will not happen if the length of b is long, due to limits on the data. For instance, each b = a(1)..a(N) will turn up in the 3 other sequences if N<29, but not if N>28. (End)

LINKS

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

Index entries for sequences that are fixed points of mappings

EXAMPLE

0 -> 01-> 010111 -> 0101110101110111.

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 1, 1, 1}}] &, {0}, 6] (* A284893 *)

Flatten[Position[s, 0]]  (* A284894 *)

Flatten[Position[s, 1]]  (* A284895 *)

CROSSREFS

Cf. A284894, A284895.

Sequence in context: A285383 A276950 A285351 * A316829 A277674 A309754

Adjacent sequences:  A284890 A284891 A284892 * A284894 A284895 A284896

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 16 2017

STATUS

approved

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Last modified November 15 06:11 EST 2019. Contains 329144 sequences. (Running on oeis4.)