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Search: id:A098280
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| A098280 |
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Front-to-back insertion-permutation sequence; contains every finite sequence of distinct positive integers. |
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+0
3
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| 1, 2, 1, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 3, 1, 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4, 4, 2, 3, 1, 2, 4, 3, 1, 2, 3, 4, 1, 2, 3, 1, 4, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4, 3, 2, 1, 3, 4, 4, 3, 1, 2, 3, 4, 1, 2, 3, 1, 4, 2, 3, 1, 2, 4, 4, 1, 3, 2, 1, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 4, 1
(list; graph; listen)
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OFFSET
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1,2
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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 before 1 and then 2 after 1, yielding 21 and 12, as well as the first 5 terms of the sequence. Next, generate the 6 permutations of 1, 2, 3 by inserting 3 into 21 and then 12, from front-to-back, like this: 321, 231, 213 then 213, 132, 123. 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,
21, 12,
321, 231, 213, 312, 132, 123, etc.
Write them in order and insert commas.
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CROSSREFS
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Cf. A098281, A030298.
Sequence in context: A004737 A014600 A165475 this_sequence A005793 A029346 A030496
Adjacent sequences: A098277 A098278 A098279 this_sequence A098281 A098282 A098283
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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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