Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M2086 #47 Sep 15 2024 07:14:40
%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
%C In an email of Aug 06 2023, Guy Chouraqui observes that the digital root of a(n) appears to be 7 for all n > 2. - _N. J. A. Sloane_, Aug 11 2023
%D R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventures in Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.
%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 Brian Hayes, <a href="https://www.jstor.org/stable/24969271">Computer Recreations: On the ups and downs of hailstone numbers</a>, Scientific American, 250 (No. 1, 1984), pp. 10-16.
%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 Peter Munn, <a href="https://oeis.org/plot2a?name1=A006884&name2=A006885&tform1=log+base+10&tform2=log+base+10&shift=0&radiop1=xy&drawpoints=true&drawlines=true">Plot2 graph of record highest point against starting value</a>
%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/pathrecs.html">3x+1 Path Records</a>
%H Robert G. Wilson v, <a href="/A006877/a006877.pdf">Letter to N. J. A. Sloane with attachments, Jan. 1989</a>
%H Robert 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_