

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
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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 Roperator 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^{L1}[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 crossreferencing 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



