A006460 Image of n after 3k iterates of '3x+1' map (k large).

1, 2, 2, 4, 4, 4, 2, 1, 2, 1, 4, 1, 1, 4, 4, 2, 1, 4, 4, 2, 2, 1, 1, 2, 4, 2, 1, 1, 1, 1, 2, 4, 4, 2, 2, 1, 1, 1, 2, 4, 2, 4, 4, 2, 2, 2, 4, 4, 1, 1, 1, 4, 4, 2, 2, 2, 4, 2, 4, 2, 2, 4, 4, 1, 1, 1, 1, 4, 4, 4, 1, 2, 2, 2, 4, 2, 2, 4, 4, 1, 2, 4, 4, 1, 1, 1, 1, 4, 1, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 4

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• R. K. Guy, Unsolved Problems in Number Theory, E16.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• M. Elia, Letter to N. J. A. Sloane, Jun. 1981
• 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

Cf. A006370, A076052 (partial sums), A139399.

Programs

Haskell

a006460 = f 0 where
   f k x | mod k 3 == 0 && x `elem` [1, 2, 4] = x
         | otherwise                          = f (k+1) (a006370 x)
-- Reinhard Zumkeller, Nov 16 2013

Mathematica

f[n_] := If[EvenQ[n], n/2, 3 n + 1];
a[n_] := With[{ff = NestWhileList[f, n, {#1, #2, #3} != {4, 2, 1}&, 3]}, ff[[Switch[Mod[Length[ff], 3], 0, -3, 1, -1, 2, -2]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Aug 08 2022 *)

Formula

For n > 2: a(n) = 4 if L = 0, otherwise L, where L = A139399(n) mod 3. - Reinhard Zumkeller, Nov 16 2013

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001