A081465 - OEIS

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 #13 Oct 29 2022 04:51:00

%S 2,5,17,353,87617,9045146753,60804857528809666817,

%T 4138643330264389621194448797227488932353,

%U 13864359953311401274177801350481278132199085263747363330276605034095638011503617

%N 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 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 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 (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 Cf. A000058, A081461, A081462, A081466.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Mar 22 2003

%E Edited and extended by _Klaus Brockhaus_, Mar 24 2003