cp's OEIS Frontend

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 A081461 #7 Dec 05 2013 19:56:01
%S A081461 1,9,103,26796621,236092315725004393,
%T A081461 3561970421302126514421966146019939188025056477849165490630219227287
%N 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.
%C A081461 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 A081461 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 A081461 (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 A081461 Cf. A000058, A081462, A081463, A081465.
%K A081461 nonn
%O A081461 1,2
%A A081461 _Amarnath Murthy_, Mar 22 2003
%E A081461 Edited and extended by _Klaus Brockhaus_, Mar 28 2003