OFFSET
1,2
COMMENTS
For the mapping g(a/b) = (a^2+b)/(a+b^2), starting with 1/2 the same procedure leads to the periodic sequence 1/2, 3/5, 1/2, 3/5, ...
MATHEMATICA
nxt[{a_, b_}]:=Module[{frac=(a^2+b^3)/(a^3+b^2)}, {Numerator[frac], Denominator[ frac]}]; Transpose[NestList[nxt, {1, 2}, 5]][[1]] (* Harvey P. Dale, Nov 09 2011 *)
PROG
(PARI) {r=1/2; for(n=1, 7, a=numerator(r); b=denominator(r); print1(a, ", "); r=(a^2+b^3)/(a^3+b^2))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 22 2003
EXTENSIONS
Edited and extended by Klaus Brockhaus, Mar 28 2003
STATUS
approved