A180853 Trajectory of 4 under map n->A006368(n).

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

Offset: 0

Author

N. J. A. Sloane, Jan 22 2011

Keywords

• nonn
• easy

Comments

The trajectory of 8 is a famous unsolved problem - see A028393.

References

• D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998; see p. 16.

Links

• J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.
• 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. A028397; A028398(3) = 4.

Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589.

Programs

Haskell

a180853 n = a180853_list !! n
a180853_list = iterate a006368 4  -- Reinhard Zumkeller, Apr 18 2012

Mathematica

Table[{4, 6, 9, 7, 5}, {21}] // Flatten   (* Jean-François Alcover, Jun 10 2013 *)
PadRight[{},120,{4,6,9,7,5}] (* Harvey P. Dale, Jul 11 2020 *)

PARI

Vec((-4-6*x-9*x^2-7*x^3-5*x^4)/((x-1)*(1+x+x^2+x^3+x^4))+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Formula

Periodic with period of length 5.

G.f.: ( -4-6*x-9*x^2-7*x^3-5*x^4 ) / ( (x-1)*(1+x+x^2+x^3+x^4) ). - R. J. Mathar, Mar 10 2011

a(n+1) = A006368(a(n)).

a(n) = a(n-5). - Wesley Ivan Hurt, Apr 26 2021