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A133162 Trajectory of 1 under the morphism 1 -> {1,1,2,1}, 2 -> {2}. 4
1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

It can be shown that this is lim_{t -> oo} S_t, where S_0 = 1, S_{t+1} = S_t S_t 2 S_t.

Suggested by A131989: a(n) = length of n-th run of 1's in A131989.

For a proof of this see the Comments of A131989. - Michel Dekking, Oct 19 2019

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for sequences that are fixed points of mappings

FORMULA

Denote the sequence by a(1), a(2), ...

Block t, that is, S_t, extends from n=1 through n=(3^(t+1)-1)/2.

Given n, to find a(n): first find t from

p = (3^t-1)/2 < n <= (3^(t+1)-1)/2.

Then if n=3^t, a(n) = 2. Otherwise, a(n) = a(n'), where

n' = n-p if n<3^t, otherwise n' = n-2p-1.

EXAMPLE

Nest[Function[l, {Flatten[(l /. {1 -> {1,1,2,1}, 2 -> {2} })] }], {1}, 5] (* Georg Fischer, Jul 19 2019 *)

CROSSREFS

Cf. A049320, A131989, A317962.

Sequence in context: A184303 A218545 A205600 * A276172 A322028 A079806

Adjacent sequences:  A133159 A133160 A133161 * A133163 A133164 A133165

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 09 2007, Oct 10 2007

STATUS

approved

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Last modified September 29 18:27 EDT 2020. Contains 337432 sequences. (Running on oeis4.)