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Search: id:A135414
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| A135414 |
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a(1)=a(2)=1 and for n>=3, a(n)=n-a(a(n-2)). |
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+0
4
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| 1, 1, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 17, 17, 17, 18, 19, 19, 20, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 34, 35, 35, 36, 37, 38, 38, 38, 39, 40, 40, 41, 42, 43, 43, 43, 44, 45, 46, 46
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A generalization of Hofstadter's G-sequence.
Contribution from Daniel Platt (d.platt(AT)web.de), Jul 27 2009: (Start)
Conjecture: A recursively built tree structure can be obtained from the sequence:
.29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45..
..|..\./...|..|...\.|./...|..|...\.|./...|..\./...|..
.18..19...20.21....22....23.24....25....26..27...28..
..\...|.../...|.....\..../...|.....|.....\...|.../...
...\..|../....|......\../....|.....|......\..|../....
.....12......13.......14....15....16........17.......
......|........\......|...../......|.........|.......
......|..........\....|.../........|.........|.......
......8...............9...........10........11.......
......|.................\......./............|.......
......|...................\.../..............|.......
......5.....................6................7.......
.........\..................|............./..........
..............\.............|........../.............
....................\.......|....../.................
............................4........................
.........................../.........................
..........................3..........................
........................./...........................
........................2............................
......................./.............................
......................1..............................
When constructing the tree node n is connected to node a(n) below:
..n..
..|..
.a(n)
Same procedure as for A005206. Reading the nodes bottom-to-top, left-to-right provides the natural numbers. The tree has a recursive structure: The following construct will give - added on top of its own ends - the above tree:
.............. ... .
............./.../..
............/.../...
. ... .....X...X....
..\...\.../.../.....
...\...\./.../......
....X...X...X.......
.....\..|../........
......\.|./.........
........X...........
(End)
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LINKS
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D. Platt, Table of n, a(n) for n=1..1999 [From Daniel Platt (d.platt(AT)web.de), Jul 27 2009]
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FORMULA
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a(n)=2+floor(n*phi)+floor((n+1)*phi)-floor((n+3)*phi) where phi=(sqrt(5)-1)/2
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PROGRAM
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(PARI) a(n)=2+floor(n*(sqrt(5)-1)/2)+floor((n+1)*(sqrt(5)-1)/2)-floor((n+3)*(sqrt(5)-1)\ /2)
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CROSSREFS
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Cf. A005206.
Sequence in context: A073425 A087876 A006158 this_sequence A140087 A099479 A120508
Adjacent sequences: A135411 A135412 A135413 this_sequence A135415 A135416 A135417
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 17 2008, Feb 19 2008
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