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

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, 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, 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

Offset

1,3

Comments

Side length of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link).

A quartic integer. - Charles R Greathouse IV, Aug 27 2017

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.2, p. 487.

Links

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

Eric Weisstein's World of Mathematics, Equilateral Triangle.

Index entries for algebraic numbers, degree 4.

Formula

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.

Equals Product_{k >= 1} 1/(1 - 1/(36*(2*k - 1)^2)). - Antonio Graciá Llorente, Mar 20 2024

From Amiram Eldar, Nov 24 2024: (Start)

Equals 2*A101263.

Equals Product_{k>=1} (1 - (-1)^k/A092242(k)). (End)

Smallest positive of the 4 real-valued roots of x^4-16*x^2+16=0. - R. J. Mathar, Aug 31 2025

Equals 1 + Product_{k=1..3} (sqrt(k+1)-sqrt(k)). - M. F. Hasler, Jun 15 2026

Example

1.03527618041008304939559535049619331339627560527972...

Mathematica

RealDigits[Sec[15 Degree], 10, 120][[1]] (* Harvey P. Dale, Jun 03 2015 *)

Prog

(PARI) sqrt(6) - sqrt(2) \\ Charles R Greathouse IV, Aug 27 2017

Crossrefs

Cf. A002193, A019679, A019691, A019884, A010464, A092242, A101263.

Sequence in context: A285297 A097465 A340272 * A210042 A338872 A274421

Adjacent sequences: A120680 A120681 A120682 * A120684 A120685 A120686

Keyword

cons,easy,nonn

Author

Rick L. Shepherd, Jun 24 2006

Status

approved