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Search: id:A135287
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| A135287 |
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a(0)=1; for n > 0, a(n) = a(n-1)+n if a(n-1) is odd, else a(n) = a(n-1)/2 . |
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+0
3
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| 1, 2, 1, 4, 2, 1, 7, 14, 7, 16, 8, 4, 2, 1, 15, 30, 15, 32, 16, 8, 4, 2, 1, 24, 12, 6, 3, 30, 15, 44, 22, 11, 43, 76, 38, 19, 55, 92, 46, 23, 63, 104, 52, 26, 13, 58, 29, 76, 38, 19, 69, 120, 60, 30, 15, 70, 35, 92, 46, 23, 83
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Let a(0), C1, C2, C be integers. Consider the sequence a(n) = a(n-1) + C1*n + C2 if a(n-1) is not divisible by C or a(n) = a(n-1)/C otherwise.
For a fixed C1, C2, C this sequence shows chaotic behavior for some a(0) and a highly regular behavior for other a(0).
The parameter C1 tells how many regular subclasses are there.
The sequence grows roughly as a(n) ~ n*const.
Here C = 2. Other sequences showing very interesting behavior have C = power of 2.
Example : C1=3, C2=10, C=3. Thus a(n)= a(n-1)+3*n+10 if a(n-1) is not divisible by 3, or a(n)= a(n-1)/3 otherwise. There are 2 classes:
a regular class with 3 subclasses (C1=3) for initial values
{a(0)=3,38,79,...}
{a(0)=1,8,12,42,47,49,63,77,88,...}
{a(0)=2,43,45,...}
and a "chaotic" class for other initial values a(0).
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MAPLE
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A135287 := proc(n) option remember ; if n = 0 then 1 ; elif A135287(n-1) mod 2 = 0 then A135287(n-1)/2 ; else n+A135287(n-1) ; fi ; end: seq(A135287(n), n=0..60) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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CROSSREFS
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Cf. A008336, A005132, A135294.
Sequence in context: A133938 A074586 A134586 this_sequence A089606 A140740 A091918
Adjacent sequences: A135284 A135285 A135286 this_sequence A135288 A135289 A135290
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KEYWORD
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nonn,easy
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AUTHOR
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Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Dec 03 2007, Dec 05 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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