### The 3x+371 Conjecture

The iterates y, t(y), t(t(y)),... of the 3x+371 function

t(x) | = | x/2 | if x is even, |

t(x) | = | (3x+371)/2 | if x is odd, |

are printed and the number of steps taken to reach one of the integers
721, 371, 265, 25, 0, -371, -563, -1855, -6307, is recorded.
It is conjectured (by Keith Matthews) that every trajectory starting from a non-zero integer will end in one of the numbers in this list and subsequently cycle. (The cycle lengths are printed in bold type.):

- 721,1267,...,1442 (
**29**)
- 371,742 (
**2**)
- 265,583,1060,530 (
**4**)
- 25,223,...,50 (
**222**)
- -371 (
**1**)
- -563,-659,-803,-1019,-1343,-1829,-2558,-1279,-1733,-2414,-1207,-1625,-2252,-1126 (
**14**)
- -1855,-2597,-3710 (
**3**)
- -6307,-9275,-13727,-20405,-30422,-15211,-22631,-33761,-50456,-25228,-12614 (
**11**)

*Last modified 15th May 2010 *

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