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A006885 Record highest point of trajectory before reaching 1 in `3x+1' problem, corresponding to starting values in A006884.
(Formerly M2086)
16

%I M2086

%S 1,2,16,52,160,9232,13120,39364,41524,250504,1276936,6810136,8153620,

%T 27114424,50143264,106358020,121012864,593279152,1570824736,

%U 2482111348,2798323360,17202377752,24648077896,52483285312,56991483520,90239155648,139646736808

%N Record highest point of trajectory before reaching 1 in `3x+1' problem, corresponding to starting values in A006884.

%C Both the 3x+1 steps and the halving steps are counted.

%C Record values in A025586: a(n) = A025586(A006884(n)) and A025586(m) < a(n) for m < A006884(n). - _Reinhard Zumkeller_, May 11 2013

%D R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventures in Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.

%D B. Hayes, Computer Recreations: On the ups and downs of hailstone numbers, Scientific American, 250 (No. 1, 1984), pp. 10-16.

%D D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.

%D G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics with Applications, 24 (1992), 79-99.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A006885/b006885.txt">Table of n, a(n) for n=1..84</a> (from Eric Roosendaal's data)

%H J. C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html">The 3x+1 problem and its generalizations</a>, Amer. Math. Monthly, 92 (1985), 3-23.

%H G. T. Leavens and M. Vermeulen, <a href="/A006877/a006877_1.pdf">3x+1 search programs</a>, Computers and Mathematics with Applications, 24 (1992), 79-99. (Annotated scanned copy)

%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/pathrecs.html">3x+1 Path Records</a>

%H R. G. Wilson, V, <a href="/A006877/a006877.pdf">Letter to N. J. A. Sloane with attachments, Jan. 1989</a>

%H R. G. Wilson, V, <a href="/A006884/a006884.pdf">Tables of A6877, A6884, A6885, Jan. 1989</a>

%H <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%t mcoll[n_]:=Max@@NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>=n&]; t={1,max=2}; Do[If[(y=mcoll[n])>max,AppendTo[t,max=y]],{n,3,10^6,4}]; t (* _Jayanta Basu_, May 28 2013 *)

%o (Haskell)

%o a006885 = a025586 . a006884 -- _Reinhard Zumkeller_, May 11 2013

%Y Cf. A006884, A006877, A006878, A033492.

%K nonn,nice

%O 1,2

%A _Robert Munafo_

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)