A028394 Iterate the map in A006369 starting at 8.

8, 11, 15, 10, 13, 17, 23, 31, 41, 55, 73, 97, 129, 86, 115, 153, 102, 68, 91, 121, 161, 215, 287, 383, 511, 681, 454, 605, 807, 538, 717, 478, 637, 849, 566, 755, 1007, 1343, 1791, 1194, 796, 1061, 1415, 1887, 1258, 1677, 1118, 1491, 994, 1325, 1767, 1178

Offset

0,1

Comments

It is an unsolved problem to determine if this sequence is bounded or unbounded.

References

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

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

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.

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

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.

Maple

G := proc(n) option remember; if n = 0 then 8 elif 4*G(n-1) mod 3 = 0 then 2*G(n-1)/3 else round(4*G(n-1)/3); fi; end; [ seq(G(i), i=0..80) ];
f:=proc(N) local n;
if N mod 3 = 0 then 2*(N/3);
elif N mod 3 = 2 then 4*((N+1)/3)-1; else
4*((N+2)/3)-3; fi; end; # N. J. A. Sloane, Feb 04 2011

Mathematica

nxt[n_]:=Module[{m=Mod[n, 3]}, Which[m==0, (2n)/3, m==1, (4n-1)/3, True, (4n+1)/3]]; NestList[nxt, 8, 60] (* Harvey P. Dale, Dec 13 2013 *)
SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n-1)/3, _, (4n+1)/3 ] }, {8}, 60] // Flatten (* Jean-François Alcover, Mar 01 2019 *)

Prog

(Haskell)
a028394 n = a028394_list !! n
a028394_list = iterate a006369 8  -- Reinhard Zumkeller, Dec 31 2011

Crossrefs

Cf. A006369, A028396, A094328, A094329, A185589, A185590.

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

Sequence in context: A279776 A101573 A029629 * A188199 A078117 A256073

Adjacent sequences: A028391 A028392 A028393 * A028395 A028396 A028397

Keyword

nonn

Author

J. H. Conway

Status

approved