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

0,2

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.

Links

Table of n, a(n) for n=0..66.

Example

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.

Sequence in context: A276800 A332684 A212809 * A029614 A143615 A199337

Adjacent sequences: A294640 A294641 A294642 * A294644 A294645 A294646

Keyword

nonn

Author

M. F. Hasler, Nov 05 2017

Status

approved