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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)
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 A349227 A264025
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 June 20 18:51 EDT 2024. Contains 373532 sequences. (Running on oeis4.)