OFFSET
1,1
COMMENTS
For the mapping g(a/b) = (a^2+b)/(a+b^2), starting with 2/1 the same procedure leads to the periodic sequence 2, 5/3, 2, 5/3, ...
MATHEMATICA
nxt[n_]:=Module[{a=Numerator[n], b=Denominator[n]}, (a^2+b^2)/(a^2-b^2)]; Numerator/@NestList[nxt, 2/1, 10] (* Harvey P. Dale, Mar 19 2011 *)
PROG
(PARI) {r=2; for(n=1, 9, a=numerator(r); b=denominator(r); print1(a, ", "); r=(a^2+b^2)/(a^2-b^2))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 22 2003
EXTENSIONS
Edited and extended by Klaus Brockhaus, Mar 24 2003
STATUS
approved