|
Search: id:A053003
|
|
|
| A053003 |
|
Continued fraction for M(1,sqrt(2)). |
|
+0
3
|
|
| 1, 5, 21, 3, 4, 14, 1, 1, 1, 1, 1, 3, 1, 15, 1, 3, 8, 36, 1, 2, 5, 2, 1, 1, 2, 2, 6, 9, 1, 1, 1, 3, 1, 2, 6, 1, 5, 1, 1, 2, 1, 13, 2, 2, 5, 1, 2, 2, 1, 5, 1, 3, 1, 3, 1, 2, 2, 2, 2, 8, 3, 1, 2, 2, 1, 10, 2, 2, 2, 3, 3, 1, 7, 1, 8, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 2, 17, 1, 4, 31, 2, 2, 5, 30, 1, 8, 2, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
M(a,b) is the limit of the arithmetic-geometric mean iteration applied repeatedly starting with a and b: a_0=a, b_0=b, a_{n+1}=(a_n+b_n)/2, b_{n+1}=sqrt(a_n*b_n).
|
|
REFERENCES
|
J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,20000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
G. Xiao, Contfrac
Index entries for continued fractions for constants
|
|
EXAMPLE
|
1.19814023473559220743992249228...
|
|
PROGRAM
|
(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(agm(1, sqrt(2))); for (n=1, 20000, write("b053003.txt", n, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 20 2009]
|
|
CROSSREFS
|
Cf. A014549, A053002, A053004.
Sequence in context: A156148 A156824 A053002 this_sequence A167202 A165204 A043053
Adjacent sequences: A053000 A053001 A053002 this_sequence A053004 A053005 A053006
|
|
KEYWORD
|
nonn,cofr,nice,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Feb 21 2000
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 22 2000
|
|
|
Search completed in 0.002 seconds
|
