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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.

%I A081465 #13 Oct 29 2022 04:51:00
%S A081465 2,5,17,353,87617,9045146753,60804857528809666817,
%T A081465 4138643330264389621194448797227488932353,
%U A081465 13864359953311401274177801350481278132199085263747363330276605034095638011503617
%N 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.
%C A081465 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, ...
%t A081465 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 *)
%o A081465 (PARI) {r=2; for(n=1,9,a=numerator(r); b=denominator(r); print1(a,","); r=(a^2+b^2)/(a^2-b^2))}
%Y A081465 Cf. A000058, A081461, A081462, A081466.
%K A081465 nonn
%O A081465 1,1
%A A081465 _Amarnath Murthy_, Mar 22 2003
%E A081465 Edited and extended by _Klaus Brockhaus_, Mar 24 2003