|
| |
|
|
A230461
|
|
Decimal expansion of AGM(sqrt(2), sqrt(3)).
|
|
1
|
|
|
|
1, 5, 6, 9, 1, 0, 5, 8, 0, 2, 8, 6, 9, 3, 2, 2, 3, 2, 6, 9, 8, 5, 1, 9, 5, 4, 5, 6, 0, 7, 8, 2, 5, 6, 1, 6, 7, 3, 1, 3, 9, 4, 5, 2, 0, 0, 0, 9, 0, 1, 7, 3, 7, 9, 6, 3, 1, 6, 8, 4, 6, 1, 9, 0, 3, 4, 2, 3, 2, 1, 6, 2, 8, 3, 2, 1, 4, 8, 9, 5, 8, 5, 2, 4, 1, 4, 4, 9, 8, 0, 5, 5, 7, 9, 0, 6, 3, 9, 0, 3, 4, 1, 0, 7, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
AGM(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.
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 1..10000
|
|
|
EXAMPLE
|
1.5691058028693223269851954560782561673139452000901737963168461903...
|
|
|
MAPLE
|
evalf(GaussAGM(sqrt(2), sqrt(3)), 120); # Muniru A Asiru, Oct 06 2018
|
|
|
MATHEMATICA
|
RealDigits[ ArithmeticGeometricMean[ Sqrt[2], Sqrt[3]], 10, 105][[1]]
|
|
|
PROG
|
(PARI) agm(sqrt(2), sqrt(3)) \\ Charles R Greathouse IV, Mar 03 2016
|
|
|
CROSSREFS
|
Cf. A014549, A053003.
Cf. A002193 (sqrt(2)), A002194 (sqrt(3)).
Sequence in context: A172997 A244274 A279664 * A277522 A019598 A340565
Adjacent sequences: A230458 A230459 A230460 * A230462 A230463 A230464
|
|
|
KEYWORD
|
nonn,cons,easy
|
|
|
AUTHOR
|
Robert G. Wilson v, Oct 19 2013
|
|
|
STATUS
|
approved
|
| |
|
|
