A028393 Iterate the map in A006368 starting at 8.

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

Offset

0,1

Comments

It is conjectured that this trajectory never repeats, but no proof of this has been found. - N. J. A. Sloane, Jul 14 2009

References

J. H. Conway, Unpredictable iterations, in Proc. Number Theory Conf., Boulder, CO, 1972, pp. 49-52. - N. J. A. Sloane, Oct 04 2012

R. K. Guy, Unsolved Problems in Number Theory, E17. - N. J. A. Sloane, Oct 04 2012

J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 5. [From N. J. A. Sloane, Jan 21 2011]

Links

Markus Sigg, Table of n, a(n) for n = 0..9999 (terms 0..1000 from T. D. Noe)

J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.

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. [From N. J. A. Sloane, Jul 14 2009]

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

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

Maple

F := proc(n) option remember; if n = 0 then 8 elif 3*F(n-1) mod 2 = 0 then 3*F(n-1)/2 else round(3*F(n-1)/4); fi; end; [ seq(F(i), i=0..80) ];

Mathematica

f[n_?EvenQ] := 3*n/2; f[n_] := Round[3*n/4]; a[0] = 8; a[n_] := a[n] = f[a[n - 1]]; Table[a[n], {n, 0, 52}]  (* Jean-François Alcover, Jun 10 2013 *)

Prog

(Haskell)
a028393 n = a028393_list !! n
a028393_list = iterate a006368 8  -- Reinhard Zumkeller, Apr 18 2012
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def F(n):
    if n == 0: return 8
    elif 3*F(n-1)%2 == 0: return 3*F(n-1)//2
    else: return (3*F(n-1)+1)//4
print([F(i) for i in range(81)]) # Michael S. Branicky, Aug 12 2021 after J. H. Conway

Crossrefs

Cf. A006368, A028394, A180864.

Cf. A028395, A180853, A182205; A028398(4) = 8.

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

Sequence in context: A308494 A087696 A293529 * A066681 A276403 A171241

Adjacent sequences: A028390 A028391 A028392 * A028394 A028395 A028396

Keyword

nonn,look

Author

J. H. Conway

Status

approved