A230461 - OEIS

%I #17 Oct 07 2018 11:19:49

%S 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,

%T 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,

%U 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

%N Decimal expansion of AGM(sqrt(2), sqrt(3)).

%C 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).

%D J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.

%H G. C. Greubel, <a href="/A230461/b230461.txt">Table of n, a(n) for n = 1..10000</a>

%e 1.5691058028693223269851954560782561673139452000901737963168461903...

%p evalf(GaussAGM(sqrt(2),sqrt(3)),120); # _Muniru A Asiru_, Oct 06 2018

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

%o (PARI) agm(sqrt(2), sqrt(3)) \\ _Charles R Greathouse IV_, Mar 03 2016

%Y Cf. A014549, A053003.

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

%K nonn,cons,easy

%O 1,2

%A _Robert G. Wilson v_, Oct 19 2013