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Search: id:A135282
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| A135282 |
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Largest k such that 2^k appears in the trajectory of the Collatz 3x+1 sequence started at n. |
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1
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| 0, 1, 4, 2, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Most of the first eighty terms in the sequence are 4, because the trajectories finish with 16->8->4->2->1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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LINKS
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Index entries related to the 3x+1 (Collatz) problem.
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EXAMPLE
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a(6)=4 because the sequence is 6,3,10,5,16,8,4,2,1.
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MAPLE
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A135282 := proc(n) local k, threen1 ; k := 0 : threen1 := n ; while threen1 > 1 do if 2^ilog[2](threen1) = threen1 then k := max(k, ilog[2](threen1)) ; fi ; if threen1 mod 2 = 0 then threen1 := threen1/2 ; else threen1 := 3*threen1+1 ; fi ; od: RETURN(k) ; end: for n from 1 to 80 do printf("%d, ", A135282(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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CROSSREFS
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Adjacent sequences: A135279 A135280 A135281 this_sequence A135283 A135284 A135285
Sequence in context: A053051 A075234 A095382 this_sequence A103859 A007400 A019921
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KEYWORD
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nonn
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AUTHOR
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Masahiko Shin (qqbf2msd(AT)etude.ocn.ne.jp), Dec 02 2007
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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