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

Author

David W. Wilson

Keywords

• nonn
• look

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.

Examples

			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.
		

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.

Crossrefs

Cf. A062052-A062059.

Column k=10 of A354236.

Programs

Haskell

import Data.List (elemIndices)
a062060 n = a062060_list !! (n-1)
a062060_list = map (+ 1) $ elemIndices 10 a078719_list
-- Reinhard Zumkeller, Oct 08 2011

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 *)

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