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A066756
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Smallest number that requires n^3 steps to reach 1 in its Collatz trajectory (counting x/2 and 3x+1 steps).
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0
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1, 2, 6, 65, 673, 342, 2919, 129991, 1590511, 301695657, 1412987847
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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R. K. Guy, Problem E16, Unsolved Problems in Number Theory, 2nd edition, Springer-Verlag, NY pp. 215-218
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LINKS
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FORMULA
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Mapping at each step for Collatz problem: x -> x/2 if n is even, else x -> 3*x+1; count the steps until x=1.
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EXAMPLE
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a(2) = 6 since the trajectory of 6 requires 2^3 = 8 steps to reach 1 (the trajectory is 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1), and 6 is the smallest number for which this is the case.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2002
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STATUS
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approved
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