A230461 Decimal expansion of AGM(sqrt(2), sqrt(3)).

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

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