A132696 Decimal expansion of 6/Pi.

1, 9, 0, 9, 8, 5, 9, 3, 1, 7, 1, 0, 2, 7, 4, 4, 0, 2, 9, 2, 2, 6, 6, 0, 5, 1, 6, 0, 4, 7, 0, 1, 7, 2, 3, 4, 4, 4, 1, 3, 5, 1, 5, 7, 4, 8, 8, 8, 5, 4, 7, 7, 3, 8, 4, 9, 7, 2, 0, 0, 8, 1, 2, 8, 7, 0, 6, 7, 6, 1, 5, 7, 1, 6, 1, 0, 7, 1, 8, 4, 2, 1, 0, 8, 1, 3, 6, 5, 6, 3, 3, 1, 9, 5, 0, 3, 7, 0, 3, 1, 4, 7, 2, 8, 7

Offset

1,2

Comments

6/Pi = Volume of the cuboid (If L1>L2>L3) / Volume of the inscribed ellipsoid.

6/Pi = Volume of the cuboid (If L1>(L2=L3)) / Volume of the inscribed spheroid.

6/Pi = Volume of the regular hexahedron (or cube) / Volume of the inscribed Sphere.

6/Pi = 1 / Arc of 30 degrees.

6/Pi = Volume of the cuboid (If L1<(L2=L3)) / Volume of the inscribed spheroid.

6/Pi = Surface area of the regular hexahedron (or cube) / surface area of the inscribed sphere.

The Eisenstein series E_2(z) = 1 - 24*Sum_{n>=1} sigma(n)*q (cf. A006352) is quasimodular form satisfying E_2((a*z+b)/(c*z+d)) = (c*z+d)^2*E_2(z) - I*(6/Pi)*c*(c*z+d). See Proposition 6 in the link of D. Zagier for a proof. - Jianing Song, Mar 24 2026

Links

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

D. Zagier, Eisenstein Series and the Discriminant Function.

Index entries for transcendental numbers

Formula

Equals Product_{k>=1} (2k+1)^3 / ( (2k)^2*(2k+3) ). - Federico Provvedi, Nov 09 2024

Example

1.90985931710274402922660516047... .

Mathematica

RealDigits[N[6/Pi, 200]] (* Erich Friedman, Mar 22 2008 *)

Prog

(PARI) 6/Pi \\ Charles R Greathouse IV, Dec 31 2011

Crossrefs

Cf. A049541, A060294, A089491, A088538, A086201, A059956.

Sequence in context: A029687 A187426 A226765 * A176523 A242400 A197264

Adjacent sequences: A132693 A132694 A132695 * A132697 A132698 A132699

Keyword

nonn,cons

Author

Omar E. Pol, Aug 26 2007, Nov 02 2007

Extensions

More terms from Erich Friedman, Mar 22 2008

Status

approved