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Search: id:A006666
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| A006666 |
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Number of halving steps to reach 1 in `3x+1' problem.
(Formerly M3733)
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+0
9
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| 0, 1, 5, 2, 4, 6, 11, 3, 13, 5, 10, 7, 7, 12, 12, 4, 9, 14, 14, 6, 6, 11, 11, 8, 16, 8, 70, 13, 13, 13, 67, 5, 18, 10, 10, 15, 15, 15, 23, 7, 69, 7, 20, 12, 12, 12, 66, 9, 17, 17, 17, 9, 9, 71, 71, 14, 22, 14, 22, 14, 14, 68, 68, 6, 19, 19, 19, 11, 11, 11, 65, 16, 73, 16, 11, 16
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Equals the total number of steps to reach 1 under the modified `3x+1' map: n -> n/2 if n is even, n -> (3n+1)/2 if n is odd.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. K. Guy, Unsolved Problems in Number Theory, E16.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
K. Matthews, The Collatz Conjecture
Eric Weisstein's World of Mathematics, Collatz Problem
Index entries for sequences related to 3x+1 (or Collatz) problem
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EXAMPLE
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2->1 so a(2) = 1; 3->10->5->16->8->4->2->1, with 5 halving steps, so a(3) = 5; 4->2->1 has two halving steps, so a(4) = 2; etc.
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CROSSREFS
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Sequence in context: A021660 A064853 A112597 this_sequence A163334 A029683 A063567
Adjacent sequences: A006663 A006664 A006665 this_sequence A006667 A006668 A006669
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. W. Gosper
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001
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