This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006884 In the `3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1. (Formerly M0843) 26

%I M0843

%S 1,2,3,7,15,27,255,447,639,703,1819,4255,4591,9663,20895,26623,31911,

%T 60975,77671,113383,138367,159487,270271,665215,704511,1042431,

%U 1212415,1441407,1875711,1988859,2643183,2684647,3041127,3873535,4637979,5656191

%N In the `3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.

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

%C Where records occur in A025586: A006885(n) = A025586(a(n)) and A025586(m) < A006885(n) for m < a(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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe and N. J. A. Sloane, <a href="/A006884/b006884.txt">Table of n, a(n) for n = 1..89</a> (from Eric Roosendaal's data, supplemented by further values from the web page of Tomás Oliveira e Silva)

%H G. T. Leavens and M. Vermeulen, <a href="http://dx.doi.org/10.1016/0898-1221(92)90034-F">3x+1 search problems</a>, Computers and Mathematics with Applications, 24 (1992), 79-99.

%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 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 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/3x_plus_1.html">Tables</a> (gives many more terms)

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

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

%t 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 *)

%o a006884 n = a006884_list !! (n-1)

%o a006884_list = f 1 0 a025586_list where

%o f i r (x:xs) = if x > r then i : f (i + 1) x xs else f (i + 1) r xs

%o -- _Reinhard Zumkeller_, May 11 2013

%o (PARI) A025586(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n)); n>>=1); r

%o r=0; for(n=1,1e6, t=A025586(n); if(t>r, r=t; print1(n", "))) \\ _Charles R Greathouse IV_, May 25 2016

%Y A060409 gives associated "dropping times", A060410 the maximal values and A060411 the steps at which the maxima occur.

%Y Cf. A006885, A006877, A006878, A033492, A060412-A060415, A132348.

%K nonn,nice,changed

%O 1,2

%A _N. J. A. Sloane_, _Robert Munafo_

%E b-file extended by _N. J. A. Sloane_, Nov 27 2007

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.