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

1,2

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, ...

Links

Table of n, a(n) for n=1..6.

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 *)

Prog

(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))}

Crossrefs

Cf. A000058, A081462, A081463, A081465.

Sequence in context: A083452 A356244 A367447 * A231646 A110698 A012485

Adjacent sequences: A081458 A081459 A081460 * A081462 A081463 A081464

Keyword

nonn

Author

Amarnath Murthy, Mar 22 2003

Extensions

Edited and extended by Klaus Brockhaus, Mar 28 2003

Status

approved