A081465 Consider the mapping f(a/b) = (a^2+b^2)/(a^2-b^2) from rationals to rationals. Starting with 2/1 (a=2, b=1) and applying the mapping to each new (reduced) rational number gives 2/1, 5/3, 17/8, 353/225, ... . Sequence gives values of the numerators.

2, 5, 17, 353, 87617, 9045146753, 60804857528809666817, 4138643330264389621194448797227488932353, 13864359953311401274177801350481278132199085263747363330276605034095638011503617

Offset: 1

Author

Amarnath Murthy, Mar 22 2003

Keywords

• nonn

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, ...

Crossrefs

Cf. A000058, A081461, A081462, A081466.

Programs

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 *)

PARI

{r=2; for(n=1,9,a=numerator(r); b=denominator(r); print1(a,","); r=(a^2+b^2)/(a^2-b^2))}

Extensions

Edited and extended by Klaus Brockhaus, Mar 24 2003