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Search: id:A098281
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| A098281 |
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Back-to-front insertion-permutation sequence; contains every finite sequence of distinct positive integers. |
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+0
3
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| 1, 1, 2, 2, 1, 1, 2, 3, 1, 3, 2, 3, 1, 2, 2, 1, 3, 2, 3, 1, 3, 2, 1, 1, 2, 3, 4, 1, 2, 4, 3, 1, 4, 2, 3, 4, 1, 2, 3, 1, 3, 2, 4, 1, 3, 4, 2, 1, 4, 3, 2, 4, 1, 3, 2, 3, 1, 2, 4, 3, 1, 4, 2, 3, 4, 1, 2, 4, 3, 1, 2, 2, 1, 3, 4, 2, 1, 4, 3, 2, 4, 1, 3, 4, 2, 1, 3, 2, 3, 1, 4, 2, 3, 4, 1, 2, 4, 3, 1, 4, 2, 3, 1, 3, 2
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Contains every finite sequence of distinct numbers...infinitely many times.
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FORMULA
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Write 1. Then place 2 after 1 and then 2 before 1, yielding 12 and 21, as well as the first 5 terms of the sequence. Next, generate the 6 permutations of 1, 2, 3 by inserting 3 into 12 and then 21, from back-to-front, like this: 123, 132, 312 then 213, 231, 321. Next, generate the 24 permutations of 1, 2, 3, 4 by inserting 4 into the permutations of 1, 2, 3. Continue forever.
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EXAMPLE
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The permutations can be written as
1,
12, 21,
123, 132, 312, 213, 231, 321, etc.
Write them in order and insert commas.
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CROSSREFS
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Cf. A098280, A030298.
Adjacent sequences: A098278 A098279 A098280 this_sequence A098282 A098283 A098284
Sequence in context: A016533 A122915 A030298 this_sequence A103343 A085263 A115092
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Sep 01 2004
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