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A321695
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For any sequence f of positive integers, let g(f) be the unique Golomb-like sequence with run lengths given by f and let k(f) be the unique Kolakoski-like sequence with run lengths given by f and initial term 1; this sequence is the unique sequence f satisfying f = g(k(f)).
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2
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1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 19, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 29, 30, 31, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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More precisely:
- g(f) is the lexicographically earliest nondecreasing sequence of positive numbers whose RUNS transform equals f,
- k(f) is the lexicographically earliest sequence of 1's and 2's whose RUNS transform equals f,
- in particular:
See A321696 for the RUNS transform of this sequence.
By applying twice the RUNS transform on this sequence, we recover the initial sequence; the same applies for A321696.
This sequence has connections with A288723; in both cases, we have sequences cyclically connected by RUNS transforms.
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LINKS
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EXAMPLE
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We can build this sequence alongside A321696 iteratively:
- this sequence starts with 1,
- hence A321696 starts with 1, 2 (after the initial run of 1's, we have a run of 2's),
- hence this sequence starts with 1, 2, 2, 3 (after the runs of 1's and 2's, we have a run of 3's),
- hence A321696 starts with 1, 2, 2, 1, 1, 2, 2, 2, 1,
- hence this sequence starts 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10,
- etc.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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