A161011 Decimal expansion of tan(1/2).

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

Offset: 0

Author

Harry J. Smith, Jun 13 2009

Keywords

• cons
• nonn

Comments

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 13 2019

Examples

			0.546302489843790513255179465780285383297551720179791246164091385932907...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• MathOverflow, What is the effect of adding 1/2 to a continued fraction?
• Wikipedia, Lindemann-Weierstrass theorem
• Index entries for transcendental numbers

Crossrefs

Cf. A019425 (continued fraction). Cf. A049471, A161011 through A161019.

Programs

Mathematica

RealDigits[N[Tan[1/2],6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *)

PARI

default(realprecision, 20080); x=10*tan(1/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b161011.txt", n, " ", d));

Formula

From Peter Bala, Nov 17 2019: (Start)

Related simple continued fraction expansions:

tan(1/2) = [0; 1, 1, 4, 1, 8, 1, 12, 1, 16, 1, 20, 1, ...]. See A019425.

2*tan(1/2) = [1, 10, 1, 3, 1, 26, 1, 7, 1, 42, 1, 11, 1, 58, 1, 15, 1, 74, 1, 19, 1, 90, ...]

(1/2)*tan(1/2) = [0; 3, 1, 1, 1, 18, 1, 5, 1, 34, 1, 9, 1, 50, 1, 13, 1, 66, 1, 17, 1, 82, ...].

tan(1/2)/(1 - tan(1/2)) = [1, 4, 1, 8, 1, 12, 1, 16, 1, 20, 1, 24, ...]

2*tan(1/2)/(1 - tan(1/2)) = [2, 2, 2, 4, 2, 6, 2, 8, 2, 10, 2, 12, ...]

4*tan(1/2)/(1 - tan(1/2)) = [4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, ...]. (End)