A062060 Numbers with 10 odd integers in their Collatz (or 3x+1) trajectory.

43, 86, 87, 89, 172, 173, 174, 177, 178, 179, 344, 346, 348, 349, 354, 355, 356, 357, 358, 385, 423, 688, 692, 693, 696, 698, 705, 708, 709, 710, 712, 714, 716, 717, 729, 761, 769, 770, 771, 777, 846, 847, 1376, 1384, 1386, 1392, 1393, 1396, 1397, 1410, 1411, 1415

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)) = 10; A006667(a(n)) = 9.

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 43 is (43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 10 odd integers.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[1000], countOdd[Collatz[#]] == 10 &] (* T. D. Noe, Dec 03 2012 *)

Prog

(Haskell)
import Data.List (elemIndices)
a062060 n = a062060_list !! (n-1)
a062060_list = map (+ 1) $ elemIndices 10 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.append(n)
            if n<2: break
        else: break
    return len([1 for i in l if i%2])
print([n for n in range(40, 1501) if a(n)==10]) # Indranil Ghosh, Apr 14 2017

Crossrefs

Cf. A062052-A062059.

Column k=10 of A354236.

Sequence in context: A247436 A063351 A065874 * A037986 A350141 A198593

Adjacent sequences: A062057 A062058 A062059 * A062061 A062062 A062063

Keyword

nonn,look

Author

David W. Wilson

Status

approved