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Decimal expansion of Pi/12.
10

%I #48 Jan 12 2024 14:31:05

%S 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,

%T 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,

%U 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

%N Decimal expansion of Pi/12.

%C Equals cone's volume (radius = 1/2, height = 1) and semi-sphere's volume (radius = 1/2). - _Eric Desbiaux_, Dec 08 2008

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

%C Multiplied by 10, decimal expansion of 5*Pi/6. - _Alonso del Arte_, Aug 19 2013

%C Volume between a cylinder and the inscribed sphere of diameter 1. - _Omar E. Pol_, Sep 25 2013

%H Ivan Panchenko, <a href="/A019679/b019679.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F A003881 - A019673. - _Omar E. Pol_, Sep 25 2013

%F Equals Integral_{x = 0..1} x^2*sqrt(1 - x^6) dx. - _Peter Bala_, Oct 27 2019

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

%F 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

%e Pi/12 = 0.2617993877991494365385536152732919070164307... - _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009

%t RealDigits[N[Pi/12, 6! ]] (* _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009 *)

%t RealDigits[Pi/12,10,120][[1]] (* _Harvey P. Dale_, Jan 12 2024 *)

%o (PARI) Pi/12 \\ _Charles R Greathouse IV_, Sep 28 2022

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

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_