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Search: id:A072761
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| A072761 |
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Minimal number of steps to reduce n to 1 using modified Collatz (or 3x+1) rule. |
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+0
1
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| 0, 1, 7, 2, 5, 8, 8, 3, 11, 5, 9, 9, 8, 9, 9, 4, 9, 12, 14, 7, 7, 11, 12, 10
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The modified rule is that you have the option to change x to 3x+1 even when x is even.
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REFERENCES
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M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002), p. 1.
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LINKS
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Index entries for sequences related to 3x+1 (or Collatz) problem
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FORMULA
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As with original Collatz problem, integers are operated on by HOTPO (halve or triple plus one) operator in either of two ways:(1) a(n) = a/2 or (2) a(n) = 3n+1
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EXAMPLE
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a(9) = 11 because tripling and adding one 3 times and then halving 8 times yields 9, 28, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1; very much faster than the original Collatz's 119 steps.
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CROSSREFS
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Cf. A008577.
Sequence in context: A093072 A066903 A074457 this_sequence A127885 A006577 A073652
Adjacent sequences: A072758 A072759 A072760 this_sequence A072762 A072763 A072764
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KEYWORD
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nonn
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AUTHOR
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Michael Joseph Halm (hierogamous(AT)lycos.com), Aug 08 2002
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