A094328 Iterate the map in A006369 starting at 4.

4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, 4, 5, 7, 9, 6

Offset: 1

Author

N. J. A. Sloane, Jun 04 2004

Keywords

• nonn
• easy

References

• J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 270.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 1).

Crossrefs

Cf. A006368, A028394-A028397, A094329, A185589, A185590.

Programs

Haskell

a094328 n = a094328_list !! (n-1)
a094328_list = iterate a006369 4  -- Reinhard Zumkeller, Dec 31 2011

Mathematica

Table[{4, 5, 7, 9, 6}, {21}] // Flatten  (* Jean-François Alcover, Jun 10 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1},{4, 5, 7, 9, 6},105] (* Ray Chandler, Sep 03 2015 *)

PARI

a(n)=([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; 1,0,0,0,0]^(n-1)*[4;5;7;9;6])[1,1] \\ Charles R Greathouse IV, Oct 18 2022

Formula

The map is: n -> if n mod 3 = 0 then 2*n/3 elif n mod 3 = 1 then (4*n-1)/3 else (4*n+1)/3.

Periodic with period length 5.