A049471 Decimal expansion of tan(1).

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

Offset: 1

Author

Albert du Toit (dutwa(AT)intekom.co.za), N. J. A. Sloane

Keywords

• cons
• easy
• nonn

Comments

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

Examples

			1.5574077246549022305...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Mohammad K. Azarian, Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, pp. 413-414.
• Mohammad K. Azarian, Solution of Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394-395.
• Index entries for transcendental numbers

Crossrefs

Cf. A093178 (continued fraction), A009001, A073449.

Programs

Mathematica

RealDigits[Tan[1], 10, 100][[1]] (* Amiram Eldar, May 15 2021 *)

PARI

default(realprecision, 20080); x=tan(1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b049471.txt", n, " ", d)); \\

Formula

Equals Sum_{k>=1} (-1)^(k+1) * B(2*k) * 2^(2*k) * (2^(2*k) - 1) / (2*k)!, where B(k) is the k-th Bernoulli number. - Amiram Eldar, May 15 2021