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A006885
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Record highest point of trajectory before reaching 1 in `3x+1' problem, corresponding to starting values in A006884.
(Formerly M2086)
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16
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1, 2, 16, 52, 160, 9232, 13120, 39364, 41524, 250504, 1276936, 6810136, 8153620, 27114424, 50143264, 106358020, 121012864, 593279152, 1570824736, 2482111348, 2798323360, 17202377752, 24648077896, 52483285312, 56991483520, 90239155648, 139646736808
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Both the 3x+1 steps and the halving steps are counted.
Record values in A025586: a(n) = A025586(A006884(n)) and A025586(m) < a(n) for m < A006884(n). - Reinhard Zumkeller, May 11 2013
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REFERENCES
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R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventures in Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.
B. Hayes, Computer Recreations: On the ups and downs of hailstone numbers, Scientific American, 250 (No. 1, 1984), pp. 10-16.
D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.
G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics with Applications, 24 (1992), 79-99.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..84 (from Eric Roosendaal's data)
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
Eric Roosendaal, 3x+1 Path Records
Index entries for sequences from "Goedel, Escher, Bach"
Index entries for sequences related to 3x+1 (or Collatz) problem
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PROG
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(Haskell)
a006885 = a025586 . a006884 -- Reinhard Zumkeller, May 11 2013
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CROSSREFS
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Cf. A006884, A006877, A006878, A033492.
Sequence in context: A058376 A120948 A090453 * A220139 A027273 A210710
Adjacent sequences: A006882 A006883 A006884 * A006886 A006887 A006888
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KEYWORD
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nonn,nice,changed
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AUTHOR
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Robert Munafo
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STATUS
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approved
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