A062057 Numbers with 7 odd integers in their Collatz (or 3x+1) trajectory.

9, 18, 19, 36, 37, 38, 72, 74, 76, 77, 81, 144, 148, 149, 152, 154, 162, 163, 288, 296, 298, 304, 308, 309, 321, 324, 325, 326, 331, 576, 592, 596, 597, 608, 616, 618, 625, 642, 643, 648, 650, 652, 653, 662, 663, 713, 715, 1152, 1184, 1192, 1194, 1216, 1232, 1236, 1237

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)) = 7; A006667(a(n)) = 6.

Examples

			The Collatz trajectory of 9 is (9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 7 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=7 of A354236.

Programs

Haskell

import Data.List (elemIndices)
a062057 n = a062057_list !! (n-1)
a062057_list = map (+ 1) $ elemIndices 7 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[#]] == 7 &] (* T. D. Noe, Dec 03 2012 *)