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.
Original entry on oeis.org
1, 9, 103, 26796621, 236092315725004393, 3561970421302126514421966146019939188025056477849165490630219227287
Offset: 1
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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 *)
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{r=1/2; for(n=1,7,a=numerator(r); b=denominator(r); print1(a,","); 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
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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 *)
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{r=2; for(n=1,9,a=numerator(r); b=denominator(r); print1(a,","); r=(a^2+b^2)/(a^2-b^2))}
A081466
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 denominators.
Original entry on oeis.org
1, 3, 8, 225, 36992, 6308330625, 21009822254496776192, 3255818067933293622186199316985612890625, 3264008661830516310447364816658205121507617681188862393654856638929469798612992
Offset: 1
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{r=2; for(n=1,9,a=numerator(r); b=denominator(r); print1(b,","); r=(a^2+b^2)/(a^2-b^2))}
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