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 (non-zero) numbers in this list and subsequently cycle. (The cycle lengths are printed in bold type.):

721,1267,...,721 (30)
371,742,371 (3)
265,583,1060,530,265 (5)
25,223,...,25 (223)
-371,-371 (2)
-563,-659,-803,-1019,-1343,-1829,-2558,-1279,-1733,-2414,-1207,-1625,-2252,-1126,-563 (15)
-1855,-2597,-3710,-1855 (4)
-6307,-9275,-13727,-20405,-30422,-15211,-22631,-33761,-50456,-25228,-12614,-6307 (12)

Enter M:

Last modified 20th January 2005
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