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Consider the mapping f(a/b) = (a^3 +b^3)/(a^2+b^2). Taking a =1, b = 2 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/2,9/5,427/53,39001680/92569,... Sequence contains the denominators.
1

%I #3 Dec 05 2013 19:56:01

%S 2,5,53,92569,1521139611842161,

%T 1759826706496123129893760473796973076447567001,

%U 5450165776683729363553774731808009059782198745252457060273092560160498157854877231868041524958184901475157837190479609639387791150077013

%N Consider the mapping f(a/b) = (a^3 +b^3)/(a^2+b^2). Taking a =1, b = 2 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/2,9/5,427/53,39001680/92569,... Sequence contains the denominators.

%C The mapping f(a/b) = (a + b)/(a - b). Taking a = 2 b = 1 to start with and carrying out this mapping repeatedly on each new (reduced)rational number gives the periodic sequence 2/1,3/1,2/1,3/1,...

%Y Cf. A081481.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Mar 24 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003