|
Search: id:A081459
|
|
|
| A081459 |
|
Consider the mapping f(r) = (1/2)*(r + N/r) from rationals to rationals where N = 5. Starting with r = 2 and applying the mapping to each new (reduced) rational number gives 2, 9/4, 161/72, 51841/23184, ..., tending to N^(1/2). Sequence gives values of the numerators. |
|
+0
3
|
|
| 2, 9, 161, 51841, 5374978561, 57780789062419261441, 6677239169351578707225356193679818792961, 89171045849445921581733341920411050611581102638589828325078491812417901966295041
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Related sequence pairs (numerator, denominator) can be obtained by choosing N = 2, 3, 6 etc.
|
|
FORMULA
|
a(n)=a(n-1)^2+5*A081460(n-1)^2 - Mario Catalani (mario.catalani(AT)unito.it), May 21 2003
|
|
EXAMPLE
|
a(n)=(1/2)(((4+2Sqrt[5])/2)^(2^(n-1))+((4-2Sqrt[5])/2)^(2^(n-1)) a(n+1)=2*a(n)^2-1 and a(1)=9 [From Artur Jasinski (grafix(AT)csl.pl), Oct 12 2008]
|
|
MATHEMATICA
|
Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 12 2008: (Start)
k = 4; Table[Simplify[Expand[(1/2) (((k + Sqrt[k^2 + 4])/2)^(2^(n - 1)) + ((k - Sqrt[k^2 + 4])/2)^(2^(n - 1)))]], {n, 1, 6}]
or
aa = {}; k = 9; Do[AppendTo[aa, k]; k = 2 k^2 - 1, {n, 1, 5}]; aa (*Artur Jasinski*) (End)
|
|
PROGRAM
|
(PARI) {r=2; N=5; for(n=1, 8, a=numerator(r); b=denominator(r); print1(a, ", "); r=(1/2)*(r + N/r) )}
|
|
CROSSREFS
|
Cf. A000129, A001333, A081460.
Sequence in context: A050995 A117116 A133468 this_sequence A038843 A053294 A078524
Adjacent sequences: A081456 A081457 A081458 this_sequence A081460 A081461 A081462
|
|
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) and Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
|
|
|
Search completed in 0.002 seconds
|
