A081461 - OEIS

A081461

Consider the mapping f(a/b) = (a^2+b^3)/(a^3+b^2) from rationals to rationals. Starting with 1/2 (a=1, b=2) and applying the mapping to each new (reduced) rational number gives 1/2, 9/5, 103/377, ... . Sequence gives values of the numerators.

%I #7 Dec 05 2013 19:56:01

%S 1,9,103,26796621,236092315725004393,

%T 3561970421302126514421966146019939188025056477849165490630219227287

%N Consider the mapping f(a/b) = (a^2+b^3)/(a^3+b^2) from rationals to rationals. Starting with 1/2 (a=1, b=2) and applying the mapping to each new (reduced) rational number gives 1/2, 9/5, 103/377, ... . Sequence gives values of the numerators.

%C 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, ...

%t 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 *)

%o (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))}

%Y Cf. A000058, A081462, A081463, A081465.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 22 2003

%E Edited and extended by _Klaus Brockhaus_, Mar 28 2003