This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A019679 #54 Feb 14 2025 17:52:52
%S A019679 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 A019679 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 A019679 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 A019679 Decimal expansion of Pi/12.
%C A019679 Equals cone's volume (radius = 1/2, height = 1) and semi-sphere's volume (radius = 1/2). - _Eric Desbiaux_, Dec 08 2008
%C A019679 Decimal expansion of least x > 0 having cos(4x) = (cos 3x)^2. See A197476. - _Clark Kimberling_, Oct 15 2011
%C A019679 Multiplied by 10, decimal expansion of 5*Pi/6. - _Alonso del Arte_, Aug 19 2013
%C A019679 Volume between a cylinder and the inscribed sphere of diameter 1. - _Omar E. Pol_, Sep 25 2013
%D A019679 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4, p. 492.
%H A019679 Ivan Panchenko, <a href="/A019679/b019679.txt">Table of n, a(n) for n = 0..1000</a>
%H A019679 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A019679 A003881 - A019673. - _Omar E. Pol_, Sep 25 2013
%F A019679 Equals Integral_{x = 0..1} x^2*sqrt(1 - x^6) dx. - _Peter Bala_, Oct 27 2019
%F A019679 Equals Sum_{k>=0} binomial(2*k,k)/((2*k+1)*4^(2*k+1)). - _Amiram Eldar_, May 30 2021
%F A019679 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 A019679 Pi/12 = 0.2617993877991494365385536152732919070164307...
%t A019679 RealDigits[N[Pi/12, 6! ]] (* _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009 *)
%t A019679 RealDigits[Pi/12,10,120][[1]] (* _Harvey P. Dale_, Jan 12 2024 *)
%o A019679 (PARI) Pi/12 \\ _Charles R Greathouse IV_, Sep 28 2022
%Y A019679 Cf. A000796, A003881, A019669, A019670, A019675, A019683, A244978.
%K A019679 nonn,cons
%O A019679 0,1
%A A019679 _N. J. A. Sloane_