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A057985 Start with 0 and repeatedly substitute: 0->01, 1->12, 2->0. 9
0, 1, 1, 2, 1, 2, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 0, 1, 1, 2, 1, 2, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 0, 1, 1, 2, 1, 2, 0, 1, 2, 0, 0, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is the fixed point of the morphism 0->01, 1->12, 2->0 starting with 0. Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2.  Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively.  Then 1/U + 1/V + 1/W = 1, where This is the fixed point of the morphism 0->01, 1->12, 2->0 starting with 0.  Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2.  Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively.  Then 1/U + 1/V + 1/W = 1, where U = 3.079595623491438786010417..., V = 2.324717957244746025960908..., W = U + 1.  If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,3,4}, and w(n) - w(n-1) is in {2,3,4,5,7}.  For n >= 1, the number of terms resulting from n iterations of the morphism is A005251(n+2).   - Clark Kimberling, May 20 2017.  If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,3,4}, and w(n) - w(n-1) is in {2,3,4,5,7}.  For n >= 1, the number of terms resulting from n iterations of the morphism is A005251(n+2). - Clark Kimberling, May 20 2017

LINKS

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

Index entries for sequences that are fixed points of mappings

MATHEMATICA

t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {0}}] &, {0}, 10] (*A057985*)

Flatten[Position[t, 0]] (*A057986*)

Flatten[Position[t, 1]] (*A057987*)

Flatten[Position[t, 2]] (*A057988*)

(* Clark Kimberling, May 13 2013 *)

CROSSREFS

Cf. A287066 (initial term 1 instead of 0).

Sequence in context: A027414 A140083 A277729 * A135387 A127442 A115628

Adjacent sequences:  A057982 A057983 A057984 * A057986 A057987 A057988

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 30 2000

STATUS

approved

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Last modified October 20 17:39 EDT 2017. Contains 293648 sequences.