A062055 Numbers with 5 odd integers in their Collatz (or 3x+1) trajectory.

11, 22, 23, 44, 45, 46, 88, 90, 92, 93, 176, 180, 181, 184, 186, 201, 352, 360, 362, 368, 369, 372, 373, 401, 402, 403, 704, 720, 724, 725, 736, 738, 739, 744, 746, 753, 802, 803, 804, 805, 806, 1408, 1440, 1448, 1450, 1472, 1476, 1477, 1478, 1488, 1492, 1493, 1506

Offset: 1

Author

David W. Wilson

Keywords

• nonn

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)) = 5; A006667(a(n)) = 4.

Examples

			The Collatz trajectory of 11 is (11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 5 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..1000
• 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-A062060.

Column k=5 of A354236.

Programs

Haskell

import Data.List (elemIndices)
a062055 n = a062055_list !! (n-1)
a062055_list = map (+ 1) $ elemIndices 5 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[2000], countOdd[Collatz[#]] == 5 &] (* T. D. Noe, Dec 03 2012 *)