A006513 Limit of the image of n after 2k iterates of `(3x+1)/2' map as k grows.

1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The map is x -> (3x+1)/2 for odd x, and x -> x/2 for even x.

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

• 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. A014682.

Programs

PARI

f(n) = if (n%2, (3*n+1)/2, n/2); \\ A014682
a(n) = my(last = n); while (1, my(new = f(f(last))); if (new == last, return(new)); last = new;); \\ Michel Marcus, Feb 03 2022

Extensions

More terms from Max Alekseyev, Oct 14 2012