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.

1, 9, 103, 26796621, 236092315725004393, 3561970421302126514421966146019939188025056477849165490630219227287

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 1/2 the same procedure leads to the periodic sequence 1/2, 3/5, 1/2, 3/5, ...

Crossrefs

Cf. A000058, A081462, A081463, A081465.

Programs

Mathematica

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 *)

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))}

Extensions

Edited and extended by Klaus Brockhaus, Mar 28 2003