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

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Gerd Lamprecht, Iterationsrechner mit Algorithmus.

Gerd Lamprecht, Zahlenfolgen (sequences).

Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean.

Example

AGM(3,3.28645055277941042287...) = Pi = A000796.

Mathematica

RealDigits[x /. FindRoot[ArithmeticGeometricMean[3, x] == Pi, {x, 4}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, May 25 2023 *)

Prog

(Other) 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;
(PARI) solve(x=3, 4, agm(3, x)-Pi) \\ Charles R Greathouse IV, Mar 03 2016

Crossrefs

Cf. A000796, A053004.

Sequence in context: A240447 A135992 A182638 * A268828 A191440 A191727

Adjacent sequences: A172081 A172082 A172083 * A172085 A172086 A172087

Keyword

cons,nonn

Author

Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Jan 25 2010

Status

approved