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A019973

Decimal expansion of tangent of 75 degrees.

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

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OFFSET

1,1

COMMENTS

An equivalent definition of this sequence: decimal expansion of x > 1 satisfying x^2 - 4*x + 1 = 0. - Arkadiusz Wesolowski, Nov 28 2011

An algebraic integer of degree 2 with minimal polynomial x^2 - 4*x + 1. - Charles R Greathouse IV, Oct 17 2016

Length of the second longest diagonal in a regular 12-gon with unit side. - Mohammed Yaseen, Dec 13 2020

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Ivan Panchenko)

Wikipedia, Exact trigonometric constants.

Index entries for algebraic numbers, degree 2.

FORMULA

Equals 2 + sqrt(3) = 2+A002194 = cotangent of 15 degrees. - Rick L. Shepherd, Jul 04 2004

Equals exp(arccosh(2)). - Amiram Eldar, Aug 07 2023

c^n = A001835(n) + (1 + sqrt(3)) * A001353(n) = A001075(n) + sqrt(3) * A001353(n); where c = 2 + sqrt(3). - Gary W. Adamson, Oct 14 2023

Equals lim_{n->oo} S(n, 4)/ S(n-1, 4), with the S-Chebyshev polynomial (see A049310) S(n, 4) = A001353(n+1). See the A001353 formula from Oct 06 2002 by Gregory V. Richardson. - Wolfdieter Lang, Nov 15 2023

Equals A019884 / A019824. - R. J. Mathar, Jan 12 2024

Equals 1/A019913. - Hugo Pfoertner, Mar 24 2024

EXAMPLE

3.732050807568877293527446341505872366942805253810380628...

MATHEMATICA

RealDigits[Tan[75 Degree], 10, 120][[1]] (* Harvey P. Dale, Nov 08 2011 *)

RealDigits[2+Sqrt[3], 10, 100][[1]] (* G. C. Greubel, Nov 20 2018 *)

PROG

(PARI) sqrt(3)+2 \\ Charles R Greathouse IV, Oct 17 2016

(Magma) SetDefaultRealField(RealField(100)); 2 + Sqrt(3); // G. C. Greubel, Nov 20 2018

(Sage) numerical_approx(2+sqrt(3), digits=100) # G. C. Greubel, Nov 20 2018

CROSSREFS