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

Author

Robert G. Wilson v, Oct 19 2013

Keywords

• nonn
• cons
• easy

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).

Examples

			1.5691058028693223269851954560782561673139452000901737963168461903...
		

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

Crossrefs

Cf. A014549, A053003.

Cf. A002193 (sqrt(2)), A002194 (sqrt(3)).

Programs

Maple

evalf(GaussAGM(sqrt(2),sqrt(3)),120); # Muniru A Asiru, Oct 06 2018

Mathematica

RealDigits[ ArithmeticGeometricMean[ Sqrt[2], Sqrt[3]], 10, 105][[1]]

PARI

agm(sqrt(2), sqrt(3)) \\ Charles R Greathouse IV, Mar 03 2016