A180864 Trajectory of 13 under map n->A006368(n).

13, 10, 15, 11, 8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, 43, 32, 48, 72, 108, 162, 243, 182, 273, 205, 154, 231, 173, 130, 195, 146, 219, 164, 246, 369, 277, 208, 312, 468, 702, 1053, 790, 1185, 889, 667, 500, 750, 1125, 844, 1266, 1899, 1424, 2136, 3204, 4806, 7209, 5407, 4055, 3041, 2281, 1711, 1283, 962

Offset: 0

Author

N. J. A. Sloane, Jan 22 2011

Keywords

• nonn

Comments

Merges with the trajectory of 8 after four steps - see A028393.

It is a famous unsolved problem to show that this trajectory is unbounded.

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

Crossrefs

Cf. A006368, A028393, A028395, A028397.

Cf. A180853, A182205.

Programs

Haskell

a180864 n = a180864_list !! n
a180864_list = iterate a006368 13  -- Reinhard Zumkeller, Apr 18 2012

Mathematica

b[n_] := If[EvenQ[n], 3n/2, Floor[(3n+2)/4]];
a[0] = 13; a[n_] := a[n] = b[a[n-1]];
Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Aug 01 2018 *)
SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {13}, 62] // Flatten (* Jean-François Alcover, Mar 01 2019 *)

Formula

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