The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A025586 Largest value in '3x+1' trajectory of n. 47
 1, 2, 16, 4, 16, 16, 52, 8, 52, 16, 52, 16, 40, 52, 160, 16, 52, 52, 88, 20, 64, 52, 160, 24, 88, 40, 9232, 52, 88, 160, 9232, 32, 100, 52, 160, 52, 112, 88, 304, 40, 9232, 64, 196, 52, 136, 160, 9232, 48, 148, 88, 232, 52, 160, 9232, 9232, 56, 196, 88, 304, 160, 184, 9232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Here by definition the trajectory ends when 1 is reached. Therefore this sequence differs for n = 1 and n = 2 from A056959, which considers the orbit ending in the infinite loop 1 -> 4 -> 2 -> 1. a(n) = A220237(n,A006577(n)). - Reinhard Zumkeller, Jan 03 2013 A006885 and A006884 give record values and where they occur. - Reinhard Zumkeller, May 11 2013 For n > 2, a(n) is divisible by 4. See the explanatory comment in A056959. - Peter Munn, Oct 14 2019 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Philippe Picart, Algorithme de Collatz et conjecture de Syracuse EXAMPLE The 3x + 1 trajectory of 9 is 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 (see A033479). Since the largest number in that sequence is 52, a(9) = 52. MATHEMATICA collatz[a0_Integer, maxits_:1000] := NestWhileList[If[EvenQ[#], #/2, 3# + 1] &, a0, Unequal[#, 1, -1, -10, -34] &, 1, maxits]; (* collatz[n] function definition by Eric Weisstein *) Flatten[Table[Take[Sort[Collatz[n], Greater], 1], {n, 60}]] (* Alonso del Arte, Nov 14 2007 *) collatzMax[n_] := Module[{r = m = n}, While[m > 2, If[OddQ[m], m = 3 * m + 1; If[m > r, r = m], m = m/2]]; r]; Table[ collatzMax[n], {n, 100}] (* Jean-François Alcover, Jan 28 2015, after Charles R Greathouse IV *) (* Using Weisstein's collatz[n] definition above *) Table[Max[collatz[n]], {n, 100}] (* Alonso del Arte, May 25 2019 *) PROG (PARI) a(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n), n/=2)); r \\ Charles R Greathouse IV, Jul 19 2011 (Haskell) a025586 = last . a220237_row -- Reinhard Zumkeller, Jan 03 2013, Aug 29 2012 (Python) def a(n):     if n<2: return 1     l=[n, ]     while True:         if n%2==0: n/=2         else: n = 3*n + 1         if not n in l:             l+=[n, ]             if n<2: break         else: break     return max(l) print [a(n) for n in range(1, 101)] # Indranil Ghosh, Apr 14 2017 (Scala) def collatz(n: Int): Int = (n % 2) match {   case 0 => n / 2   case 1 => 3 * n + 1 } def collatzTrajectory(start: Int): List[Int] = if (start == 1) List(1) else {   import scala.collection.mutable.ListBuffer   var curr = start; var trajectory = new ListBuffer[Int]()   while (curr > 1) { trajectory += curr; curr = collatz(curr) }   trajectory.toList } for (n <- 1 to 100) yield collatzTrajectory(n).max // Alonso del Arte, Jun 02 2019 CROSSREFS Essentially the same as A056959: only a(1) and a(2) differ, see Comments. Cf. A006370, A006577, A006884, A006885, A220237. Sequence in context: A076536 A110009 A232503 * A087251 A211367 A220314 Adjacent sequences:  A025583 A025584 A025585 * A025587 A025588 A025589 KEYWORD nonn,nice,look AUTHOR STATUS approved

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

Last modified January 20 11:01 EST 2020. Contains 331083 sequences. (Running on oeis4.)