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A288724 Second sequence of a Kolakoski 3-Ouroboros, i.e., sequence of 1s, 2s and 3s that is second in a chain of three distinct sequences where successive run-length encodings produce seq(1) -> seq(2) -> seq(3) -> seq(1). 4
2, 2, 2, 3, 1, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 3, 1, 2, 2, 3, 3, 1, 1, 2, 2, 2, 3, 1, 1, 2, 2, 2, 3, 3, 3, 1, 2, 3, 1, 1, 2, 2, 2, 3, 1, 2, 2, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 2, 3, 1, 1, 2, 2, 3, 3, 1, 1, 1, 2, 3, 3, 1, 1, 1, 2, 2, 2, 3, 1, 2, 2, 3, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See comments at A288723.

LINKS

Georg Fischer, Table of n, a(n) for n = 1..2000 (recovered b-file, Jan 16 2019)

Rémy Sigrist, PARI program for A288723, A288724 and A288725

EXAMPLE

Write down the run-lengths of the sequence A288723, or the lengths of the runs of 1s, 2s and 3s. This yields a second and different sequence of 1s, 2s and 3s, A288724 (as above). The run-lengths of this second sequence yield a third and different sequence, A288725. The run-lengths of this third sequence yield the original sequence. For example, bracket the runs of distinct integers, then replace the original digits with the run-lengths to create the second sequence:

(1,1), (2,2), (3,3), (1,1,1), (2), (3), (1,1), (2,2), (3,3,3), (1,1,1), (2,2,2), (3), (1), (2), (3,3), (1,1,1), (2), (3,3), (1,1), (2,2,2), ... -> 2, 2, 2, 3, 1, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 3, 1, 2, 2, 3, ...

Apply the same process to the second sequence and the third sequence appears:

(2,2,2), (3), (1,1), (2,2), (3,3,3), (1,1,1), (2), (3), (1), (2,2), (3,3), (1,1), (2,2,2), (3), (1,1), (2,2,2), (3,3,3), (1), (2), (3), ... -> 3, 1, 2, 2, 3, 3, 1, 1, 1, 2, 2, 2, 3, 1, 2, 3, 3, 1, 1, 1, ...

Apply the same process to the third sequence and the original sequence reappears:

(3), (1), (2,2), (3,3), (1,1,1), (2,2,2), (3), (1), (2), (3,3), (1,1,1), (2), (3), (1,1), (2,2), (3,3,3), (1,1,1), (2,2,2), (3), (1), ... -> 1, 1, 2, 2, 3, 3, 1, 1, 1, 2, 3, 1, 1, 2, 2, 3, 3, 3, 1, 1, ...

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000002, A025142, A025143. A288723 and A288725 are the first and third sequences in this 3-Ouroboros.

Sequence in context: A106795 A162203 A071455 * A198862 A264025 A139465

Adjacent sequences:  A288721 A288722 A288723 * A288725 A288726 A288727

KEYWORD

nonn

AUTHOR

Anthony Sand, Jun 14 2017

EXTENSIONS

Data corrected by Rémy Sigrist, Oct 07 2017

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)