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Search: id:A075684
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| A075684 |
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For odd numbers 2n-1, the maximum number produced by iterating the reduced Collatz function R defined as R(k) = (3k+1)/2^r, with r as large as possible. |
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2
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| 1, 5, 5, 17, 17, 17, 13, 53, 17, 29, 21, 53, 29, 3077, 29, 3077, 33, 53, 37, 101, 3077, 65, 45, 3077, 49, 77, 53, 3077, 65, 101, 61, 3077, 65, 101, 69, 3077, 3077, 113, 77, 269, 81, 3077, 85, 197, 101, 3077, 93, 3077, 3077, 149, 101, 3077, 269, 3077, 3077, 3077
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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See A075677 for the function R applied to the odd numbers once. See A075680 for the number of iterations required to yield 1. Sequence A006884, with the number 2 removed, gives the odd numbers that produce new record maxima. The maxima of the current sequence are related to A006885: if m is a maximum of the usual Collatz iteration, then (m-1)/3 is the maximum for the reduced Collatz iteration.
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EXAMPLE
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a(4) = 17 because 7 is the fourth odd number and 17 is the largest number in the iteration: R(7)=11, R(11)=17, R(17)=13, R(13)=5, R(5)=1.
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MATHEMATICA
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nextOddK[n_] := Module[{m=3n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[m=n; maxK=n; If[n>1, While[m=nextOddK[m]; maxK=Max[m, maxK]; m!=1]]; maxK, {n, 1, 200, 2}]
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CROSSREFS
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Cf. A006884, A006885, A075677, A075680.
Sequence in context: A072272 A079317 A125256 this_sequence A146876 A147206 A146852
Adjacent sequences: A075681 A075682 A075683 this_sequence A075685 A075686 A075687
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KEYWORD
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easy,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 25 2002
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