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

1,1

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).

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A140076 A135186 A011336 * A081095 A080596 A376598

Adjacent sequences: A094325 A094326 A094327 * A094329 A094330 A094331

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 04 2004

Status

approved