The 3x+371 Conjecture
The iterates y, t(y), t(t(y)),... of the 3x+371 function
\[
t(x)=\left\{\begin{array}{ccc}
x/2 &\mbox{if $x ≡ 0 \pmod{2}$,}\\
(3x+371)/2&\mbox{if $x ≡ 1 \pmod{2}$}
\end{array}
\right.
\]
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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