cp's OEIS Frontend

A120683 Decimal expansion of secant of 15 degrees (cosecant of 75 degrees).

%I A120683 #28 Aug 31 2025 13:40:48
%S A120683 1,0,3,5,2,7,6,1,8,0,4,1,0,0,8,3,0,4,9,3,9,5,5,9,5,3,5,0,4,9,6,1,9,3,
%T A120683 3,1,3,3,9,6,2,7,5,6,0,5,2,7,9,7,2,2,0,5,5,2,5,6,0,1,2,8,2,9,2,6,0,2,
%U A120683 2,7,8,9,8,9,9,5,2,0,7,9,8,7,6,8,9,4,7,1,8,9,8,7,7,6,9,9,8,6,6,2,0,8,3,5,8
%N A120683 Decimal expansion of secant of 15 degrees (cosecant of 75 degrees).
%C A120683 Side length of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link).
%C A120683 A quartic integer. - _Charles R Greathouse IV_, Aug 27 2017
%D A120683 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.2, p. 487.
%H A120683 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EquilateralTriangle.html">Equilateral Triangle</a>.
%H A120683 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A120683 Equals sec(Pi/12) = sec(A019679) = sqrt(6) - sqrt(2) = A010464 - A002193 = csc(5*Pi/12) = 1/sin(5*Pi/12) = 1/sin(10*A019691) = 1/A019884.
%F A120683 Equals Product_{k >= 1} 1/(1 - 1/(36*(2*k - 1)^2)). - _Antonio Graciá Llorente_, Mar 20 2024
%F A120683 From _Amiram Eldar_, Nov 24 2024: (Start)
%F A120683 Equals 2*A101263.
%F A120683 Equals Product_{k>=1} (1 - (-1)^k/A092242(k)). (End)
%F A120683 Smallest positive of the 4 real-valued roots of x^4-16*x^2+16=0. - _R. J. Mathar_, Aug 31 2025
%e A120683 1.03527618041008304939559535049619331339627560527972...
%t A120683 RealDigits[Sec[15 Degree],10,120][[1]] (* _Harvey P. Dale_, Jun 03 2015 *)
%o A120683 (PARI) sqrt(6) - sqrt(2) \\ _Charles R Greathouse IV_, Aug 27 2017
%Y A120683 Cf. A002193, A019679, A019691, A019884, A010464, A092242, A101263.
%K A120683 cons,easy,nonn,changed
%O A120683 1,3
%A A120683 _Rick L. Shepherd_, Jun 24 2006