A019679 Decimal expansion of Pi/12.

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

Offset

0,1

Comments

Equals cone's volume (radius = 1/2, height = 1) and semi-sphere's volume (radius = 1/2). - Eric Desbiaux, Dec 08 2008

Decimal expansion of least x > 0 having cos(4x) = (cos 3x)^2. See A197476. - Clark Kimberling, Oct 15 2011

Multiplied by 10, decimal expansion of 5*Pi/6. - Alonso del Arte, Aug 19 2013

Volume between a cylinder and the inscribed sphere of diameter 1. - Omar E. Pol, Sep 25 2013

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4, p. 492.

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for transcendental numbers.

Formula

A003881 - A019673. - Omar E. Pol, Sep 25 2013

Equals Integral_{x = 0..1} x^2*sqrt(1 - x^6) dx. - Peter Bala, Oct 27 2019

Equals Sum_{k>=0} binomial(2*k,k)/((2*k+1)*4^(2*k+1)). - Amiram Eldar, May 30 2021

Constant divided by 10 = Pi/120 = 0.0261799387... = Sum_{n = -oo..oo} 1/((4*n+1)*(4*n+2)*(4*n+3)*(4*n+5)*(4*n+6)*(4*n+7)) (using the Eisenstein summation convention Sum_{n = -oo..oo} = lim_{N -> oo} Sum_{n = -N..N}). Note that 22/7 - Pi = 240*Sum_{n >= 1} 1/((4*n+1)*(4*n+2)*(4*n+3)*(4*n+5)*(4*n+6)*(4*n+7)). - Peter Bala, Nov 28 2021

Example

Pi/12 = 0.2617993877991494365385536152732919070164307... - Vladimir Joseph Stephan Orlovsky, Dec 02 2009

Mathematica

RealDigits[N[Pi/12, 6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)
RealDigits[Pi/12, 10, 120][[1]] (* Harvey P. Dale, Jan 12 2024 *)

Prog

(PARI) Pi/12 \\ Charles R Greathouse IV, Sep 28 2022

Crossrefs

Cf. A000796, A003881, A019669, A019670, A019675, A019683, A244978.

Sequence in context: A199501 A021386 A201936 * A104457 A155832 A136764

Adjacent sequences: A019676 A019677 A019678 * A019680 A019681 A019682

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved