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A006884
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In the `3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.
(Formerly M0843)
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21
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1, 2, 3, 7, 15, 27, 255, 447, 639, 703, 1819, 4255, 4591, 9663, 20895, 26623, 31911, 60975, 77671, 113383, 138367, 159487, 270271, 665215, 704511, 1042431, 1212415, 1441407, 1875711, 1988859, 2643183, 2684647, 3041127, 3873535, 4637979, 5656191
(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.
Where records occur in A025586: A006885(n) = A025586(a(n)) and A025586(m) < A006885(n) for m < a(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 and N. J. A. Sloane, Table of n, a(n) for n=1..89 (from Eric Roosendaal's data, supplemented by further values from the web page of Tomas Oliveira e Silva)
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
Tomas Oliveira e Silva, Tables (gives many more terms)
Eric Roosendaal, 3x+1 Path Records
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for sequences from "Goedel, Escher, Bach"
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PROG
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(Haskell)
a006884 n = a006884_list !! (n-1)
a006884_list = f 1 0 a025586_list where
f i r (x:xs) = if x > r then i : f (i + 1) x xs else f (i + 1) r xs
-- Reinhard Zumkeller, May 11 2013
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CROSSREFS
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A060409 gives associated "dropping times", A060410 the maximal values and A060411 the steps at which the maxima occur.
Cf. A006885, A006877, A006878, A033492, A060412-A060415, A132348.
Sequence in context: A066044 A066460 A001276 * A074742 A020873 A049958
Adjacent sequences: A006881 A006882 A006883 * A006885 A006886 A006887
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KEYWORD
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nonn,nice,easy,changed
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AUTHOR
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N. J. A. Sloane, Robert Munafo
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EXTENSIONS
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b-file extended by N. J. A. Sloane, Nov 27 2007
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STATUS
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approved
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