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A025586 Largest value in '3x+1' trajectory of n. 46
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

Index entries for sequences related to 3x+1 (or Collatz) problem

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-Fran├žois 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 xrange(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,changed

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)