cp's OEIS Frontend

A172084 Decimal expansion of the constant x that satisfies Arithmetic-Geometric-Mean(3,x) = Pi.

%I A172084 #11 Feb 16 2025 08:33:11
%S A172084 3,2,8,6,4,5,0,5,5,2,7,7,9,4,1,0,4,2,2,8,7,8,2,5,7,1,9,3,7,7,2,9,2,9,
%T A172084 0,6,5,3,1,4,7,4,4,5,2,1,4,0,2,6,7,4,2,2,4,4,0,3,0,5,5,1,8,7,7,4,4,6,
%U A172084 8,3,6,1,9,7,8,8,3,3,1,8,5,4,4,5,7,7,3,0,7,8,8,9,8,1,1,8,9,6,0,0,4,9,3,1,5
%N A172084 Decimal expansion of the constant x that satisfies Arithmetic-Geometric-Mean(3,x) = Pi.
%H A172084 Gerd Lamprecht, <a href="http://www.gerdlamprecht.de/Roemisch_JAVA.htm">Iterationsrechner mit Algorithmus</a>.
%H A172084 Gerd Lamprecht, <a href="http://www.gerdlamprecht.de/Zahlenfolgen.html">Zahlenfolgen (sequences)</a>.
%H A172084 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Arithmetic-GeometricMean.html">Arithmetic-Geometric Mean</a>.
%e A172084 AGM(3,3.28645055277941042287...) = Pi = A000796.
%t A172084 RealDigits[x /. FindRoot[ArithmeticGeometricMean[3, x] == Pi, {x, 4}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, May 25 2023 *)
%o A172084 (Gerd Lamprecht online Iterationsrechner) ##@N@C0]='50';@C1]=MitGenau('3.286450552779410422878257193772929',@C0]);@B0]='1.0';aD[0]='0.'+addstr('0',@U@C0])-2)+'1';IM=2; @N@Bi]=bigc(1,GetKoDezi(796,0,@U@C0])),bigc(19,'3.0',@C1]));@Bi]=bigc(2, @Bi],'2.045601998');@C1]=bigc(0,@C1],@Bi]);@Nbigc(5,bigc(6,@Bi],@C0]), aD[0])%3C0@N0@N1@Nif(i%3C2)i=2;
%o A172084 (PARI) solve(x=3,4,agm(3,x)-Pi) \\ _Charles R Greathouse IV_, Mar 03 2016
%Y A172084 Cf. A000796, A053004.
%K A172084 cons,nonn
%O A172084 1,1
%A A172084 Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Jan 25 2010