A062058 Numbers with 8 odd integers in their Collatz (or 3x+1) trajectory.

25, 49, 50, 51, 98, 99, 100, 101, 102, 196, 197, 198, 200, 202, 204, 205, 217, 392, 394, 396, 397, 400, 404, 405, 408, 410, 433, 434, 435, 441, 475, 784, 788, 789, 792, 794, 800, 808, 810, 816, 820, 821, 833, 857, 866, 867, 868, 869, 870, 875, 882, 883, 950, 951, 953

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)) = 8; A006667(a(n)) = 7.

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.

Example

The Collatz trajectory of 25 is (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 8 odd integers.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[1000], countOdd[Collatz[#]] == 8 &] (* T. D. Noe, Dec 03 2012 *)

Prog

(Haskell)
import Data.List (elemIndices)
a062058 n = a062058_list !! (n-1)
a062058_list = map (+ 1) $ elemIndices 8 a078719_list
-- Reinhard Zumkeller, Oct 08 2011

Crossrefs

Cf. A062052-A062060.

Column k=8 of A354236.

Sequence in context: A284666 A090093 A004936 * A273510 A198591 A069063

Adjacent sequences: A062055 A062056 A062057 * A062059 A062060 A062061

Keyword

nonn

Author

David W. Wilson

Status

approved