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Search: id:A007062
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| A007062 |
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Let P(n) of a sequence s(1),s(2),s(3),... be obtained by leaving s(1),...,s(n) fixed and reversing every n consecutive terms thereafter; apply P(2) to 1,2,3,... to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) is A007062.
(Formerly M0966)
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+0
1
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| 1, 2, 4, 5, 7, 12, 14, 15, 23, 28, 30, 41, 43, 48, 56, 67, 69, 84, 86, 87, 111, 116, 124, 139, 141, 162, 180, 181, 183, 224, 232, 237, 271, 276, 278, 315, 333, 338, 372, 383, 385, 426, 428, 439, 473, 478, 538, 543, 551, 556, 620
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Comment from Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Aug 05 2004: (Start) Consider the following array:
.1..2..3..4..5..6..7..8..9.10.11.12.13.14.15.16.17.18.19.20
.2..1..4..3..6..5..8..7.10..9.12.11.14.13.16.15.18.17.20.19
.4..1..2..5..6..3.10..7..8.11.12..9.16.13.14.17.18.15.22.19
.5..2..1..4..7.10..3..6..9.12.11..8.17.14.13.16.19.22.15.18
.7..4..1..2..5.12..8..6..3.10.13.14.17..8.11.18.15.22.19.16
12..5..2..1..4..7.14.13.10..3..6..8.22.15.18.11..8.17.24.23
14..7..4..1..2..5.12.15.22..8..6..3.10.13.20.23.24.17..8.11
15.12..5..2..1..4..7.14.23.20.13.10..3..6..8.22.25.28.31.18
23.14..7..4..1..2..5.12.15.28.25.22..8..6..3.10.13.20.33.30
28.15.12..5..2..1..4..7.14.23.30.33.20.13.10..3..6..8.22.25
which is formed as follows: . first row is the positive integers
. second row: group the first row in pairs of two and reverse the order within groups; e.g. 1 2 -> 2 1 and 3 4 -> 4 3
. n-th row: group the n-1th row in groups of n and reverse the order within groups
The sequence A007062 is the first column of this array, as well as the diagonal excluding the diagonal's first term. It is also various other 'partial columns' and 'partial diagonals'.
To calculate the i-th column/jth row value, one can work backwards to find which column of the first row it came from. For each row, first reverse its position within the group then go up. It appears lim n->infinity a(n)/n^2 exists and is ~ .22847 ~ sqrt(.0522) (end)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Problem E3163, Amer. Math. Monthly, 96 (1989), 57.
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EXAMPLE
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PS(2) begins with 1,2,4,3,6,5,8; PS(3) with 1,2,4,5,6,3,10; PS(4) with 1,2,4,5,7,10,3.
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CROSSREFS
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Cf. A057030 (here we have "s(1), ..., s(n)", whereas 057030 has "s(1), ..., s(n-1)").
Sequence in context: A090649 A154686 A165196 this_sequence A121817 A116432 A050027
Adjacent sequences: A007059 A007060 A007061 this_sequence A007063 A007064 A007065
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
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More terms and better description from Clark Kimberling, Jul 28, 2000.
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