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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.
2

%I #5 Dec 05 2013 19:56:01

%S 1,3,8,225,36992,6308330625,21009822254496776192,

%T 3255818067933293622186199316985612890625,

%U 3264008661830516310447364816658205121507617681188862393654856638929469798612992

%N 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.

%o (PARI) {r=2; for(n=1,9,a=numerator(r); b=denominator(r); print1(b,","); r=(a^2+b^2)/(a^2-b^2))}

%Y Cf. A000058, A081461, A081462, A081465.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 22 2003

%E Edited and extended by _Klaus Brockhaus_, Mar 24 2003