_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Mar 24 2003

Consider the mapping f(a/b) = (a^2 +b^2)/(a+b). Taking a =1, b = 2 to start with, and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/2,5/3,17/4,305/21,... Sequence contains the denominators.

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,...

nonn,new

nonn

Consider the mapping f(a/b) = (a^2 +b^2)/(a+b). Taking a =1, b = 2 to start with, and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/2,5/3,17/4,305/21,... Sequence contains the denominators.

2, 3, 4, 21, 163, 23448, 1092023377, 596231923288918561, 355492505697703670063523236830811569, 126374921607231876111985200006557923908784362170241984606666354067170697

1,1

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,...

Cf. A081479.

nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 24 2003

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

approved