OFFSET
1,1
COMMENTS
It is provable that (beyond 1 and 2) the largest peak value in any 3x+1 (Collatz) trajectory must be a multiple of 4. However, an infinite number of multiples of 4 exist that cannot be the largest peak value of such a trajectory. E.g., no integer of the form 16k+12 = 4*(4k+3) (where k is a nonnegative integer) can be a largest peak value, because the trajectory immediately after the value 16k+12 would consist of the values 8k+6, 4k+3, 12k+10, 6k+5, and 18k+16, which exceeds 16k+12.
LINKS
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 08 2003
EXTENSIONS
Definition and example reworded by Jon E. Schoenfield, Sep 01 2013
STATUS
approved