A081462
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 denominators.
Original entry on oeis.org
2, 5, 377, 617428, 19241552119440973526245, 6579843627298148620615676439841151690983233028443241
Offset: 1
-
{r=1/2; for(n=1,7,a=numerator(r); b=denominator(r); print1(b,","); r=(a^2+b^3)/(a^3+b^2))}
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.
Original entry on oeis.org
2, 5, 17, 353, 87617, 9045146753, 60804857528809666817, 4138643330264389621194448797227488932353, 13864359953311401274177801350481278132199085263747363330276605034095638011503617
Offset: 1
-
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 *)
-
{r=2; for(n=1,9,a=numerator(r); b=denominator(r); print1(a,","); r=(a^2+b^2)/(a^2-b^2))}
Showing 1-2 of 2 results.
Comments