A062059 Numbers with 9 odd integers in their Collatz (or 3x+1) trajectory.

33, 65, 66, 67, 130, 131, 132, 133, 134, 260, 261, 262, 264, 266, 268, 269, 273, 289, 520, 522, 524, 525, 528, 529, 532, 533, 536, 538, 546, 547, 555, 571, 577, 578, 579, 583, 633, 635, 1040, 1044, 1045, 1048, 1050, 1056, 1058, 1059, 1064, 1066, 1072, 1076, 1077

Offset

1,1

Comments

The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd.

The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.

A078719(a(n)) = 9; A006667(a(n)) = 8.

References

J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

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

Index entries for 2-automatic sequences.

Example

The Collatz trajectory of 33 is (33, 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 9 odd integers.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[1000], countOdd[Collatz[#]] == 9 &] (* T. D. Noe, Dec 03 2012 *)

Prog

(Haskell)
import Data.List (elemIndices)
a062059 n = a062059_list !! (n-1)
a062059_list = map (+ 1) $ elemIndices 9 a078719_list
-- Reinhard Zumkeller, Oct 08 2011
(Python)
def a(n):
    l=[n, ]
    while True:
        if n%2==0: n//=2
        else: n = 3*n + 1
        if n not in l:
            l+=[n, ]
            if n<2: break
        else: break
    return len([i for i in l if i%2])
[n for n in range(30, 1101) if a(n)==9] # Indranil Ghosh, Apr 14 2017

Crossrefs

Cf. A062052, A062053, A062054, A062055, A062056, A062057, A062058, A062060.

Column k=9 of A354236.

Sequence in context: A183347 A116350 A331071 * A285317 A198592 A325377

Adjacent sequences: A062056 A062057 A062058 * A062060 A062061 A062062

Keyword

nonn

Author

David W. Wilson

Status

approved