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Search: id:A081465
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| A081465 |
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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 numerators. |
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3
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| 2, 5, 17, 353, 87617, 9045146753, 60804857528809666817, 4138643330264389621194448797227488932353, 13864359953311401274177801350481278132199085263747363330276605034095638011503617
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For the mapping g(a/b) = (a^2+b)/(a+b^2), starting with 2/1 the same procedure leads to the periodic sequence 2, 5/3, 2, 5/3, ...
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PROGRAM
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(PARI) {r=2; for(n=1, 9, a=numerator(r); b=denominator(r); print1(a, ", "); r=(a^2+b^2)/(a^2-b^2))}
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CROSSREFS
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Cf. A000058, A081461, A081462, A081466.
Sequence in context: A132198 A111635 A041455 this_sequence A128000 A124374 A113617
Adjacent sequences: A081462 A081463 A081464 this_sequence A081466 A081467 A081468
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2003
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 24 2003
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