A294643 Length (= size) of the orbit of n under the "3x+1" map A006370: x -> x/2 if even, 3x+1 if odd. a(n) = -1 in case the orbit would be infinite.

1, 3, 3, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, 18, 18, 5, 13, 21, 21, 8, 8, 16, 16, 11, 24, 11, 112, 19, 19, 19, 107, 6, 27, 14, 14, 22, 22, 22, 35, 9, 110, 9, 30, 17, 17, 17, 105, 12, 25, 25, 25, 12, 12, 113, 113, 20, 33, 20, 33, 20, 20, 108, 108, 7, 28, 28

Offset: 0

Author

M. F. Hasler, Nov 05 2017

Keywords

• nonn

Comments

The orbit of x under f is O(x; f) = { f^k(x); k = 0, 1, 2, ... }, i.e., the set of all points in the trajectory of x under iterations of f.

The famous "3x+1 problem" or Collatz conjecture (also attributed to other names) states that for f = A006370, the trajectory (f^k(x); k >= 0) always ends in the cycle 1 -> 4 -> 2 -> 1, for any integer starting value x >= 0.

Examples

			a(0) = 1 = # { 0 }, since 0 -> 0 -> 0 ... under A006370.
a(1) = 3 = # { 1, 4, 2 }, since 1 -> (3*1 + 1 =) 4 -> 2 -> 1 -> 4 etc. under A006370.
a(3) = 8 = # { 3, 10, 5, 16, 8, 4, 2, 1 }, since 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 -> 4 etc. under A006370.
		

Crossrefs

Cf. A006370 (Collatz or 3x+1 map), A008908 (number of steps to reach 1), A174221 (the "PrimeLatz" map: add 3 next primes), A293980, A293975 (variant: add the next prime), A293982.