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A028394 Iterate the map in A006369 starting at 8. 20
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 (list; graph; refs; listen; history; text; internal format)
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
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.
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
Sequence in context: A279776 A101573 A029629 * A188199 A078117 A256073
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 15 18:28 EDT 2024. Contains 371696 sequences. (Running on oeis4.)