|
| |
|
|
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.
|
|
2
| |
|
|
2, 5, 17, 353, 87617, 9045146753, 60804857528809666817, 4138643330264389621194448797227488932353, 13864359953311401274177801350481278132199085263747363330276605034095638011503617
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| 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, ...
|
|
|
MATHEMATICA
| nxt[n_]:=Module[{a=Numerator[n], b=Denominator[n]}, (a^2+b^2)/(a^2-b^2)]; Numerator/@NestList[nxt, 2/1, 10] {* From Harvey P. Dale, Mar 19 2011 *)
|
|
|
PROG
| (PARI) {r=2; for(n=1, 9, a=numerator(r); b=denominator(r); print1(a, ", "); r=(a^2+b^2)/(a^2-b^2))}
|
|
|
CROSSREFS
| Cf. A000058, A081461, A081462, A081466.
Sequence in context: A132198 A111635 A041455 * A128000 A124374 A113617
Adjacent sequences: A081462 A081463 A081464 * A081466 A081467 A081468
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2003
|
|
|
EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 24 2003
|
| |
|
|
