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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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24
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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
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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.
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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.
D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.
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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G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics with Applications, 24 (1992), 79-99.
G. T. Leavens and M. Vermeulen, 3x+1 search programs, Computers and Mathematics with Applications, 24 (1992), 79-99. (Annotated scanned copy)
Tomás Oliveira e Silva, Tables (gives many more terms).
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MATHEMATICA
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mcoll[n_]:=Max@@NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; t={1, max=2}; Do[If[(y=mcoll[n])>max, max=y; AppendTo[t, n]], {n, 3, 705000, 4}]; t (* Jayanta Basu, May 28 2013 *)
DeleteDuplicates[Parallelize[Table[{n, Max[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]]}, {n, 57*10^5}]], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Apr 23 2023 *)
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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
(PARI) A025586(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n)); n>>=1); r
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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.
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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