A006460 Image of n after 3k iterates of '3x+1' map (k large). (Formerly M0304)

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

1,2

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

Formula

For n > 2: a(n) = 4 if L = 0, otherwise L, where L = A139399(n) mod 3. - 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 *)

Prog

(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

Crossrefs

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

Sequence in context: A231731 A143358 A143729 * A064137 A329588 A104202

Adjacent sequences: A006457 A006458 A006459 * A006461 A006462 A006463

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved