OFFSET
1,2
COMMENTS
Take any pair {a,b}. Each next pair is get by the rule {a,b} -> Sort[{Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]]. Here k=3 and the first {a,b}={1,2}. For k = 2 there is a fixed point {a,b=2a}. For k > 2, are there any limits or cycles of the sequence {for some initial pair {a,b}?
FORMULA
EXAMPLE
3rd pair is {2,3} because 2nd pair is {1,3}, Max[{a,b}]-Min[{a,b}] = 3 - 1 = 2, 3*Min[{a,b}] = 3*1 = 3.
MATHEMATICA
ss=Table[0, {j, 100}]; s=ss[[1]]={1, 2}; Do[ss[[i]]=Sort[{Max[s]-Min[s], 3*Min[s]}]; s=ss[[i]], {i, 2, 100}]; Flatten[ss]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Zak Seidov, Sep 10 2002
STATUS
approved