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
Keywords
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
Crossrefs
Programs
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Haskell
a028394 n = a028394_list !! n a028394_list = iterate a006369 8 -- Reinhard Zumkeller, Dec 31 2011
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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
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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 *)
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.
Comments