A121224 Decimal expansion of 1/(2*tan(1/2)).

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

Offset

0,1

Comments

The divergent series Sum_{n>=1} sin(n) sums to this value if interpreted as a geometric series; that is, Sum_{n>=1} sin(n) = Im(Sum_{n>=1} e^(ni)) = Im(-e^i/(e^i-1)) = 1/(2*tan(1/2)). If x_m = Sum_{0<n<m} sin(n), then (max(x_1, x_2, ...) + min(x_1, x_2, ...))/2 tends to this number. Given by the series 1+Sum_{n>=1} (-1)^n B_(2n)/(2n)!. Corresponding value for cos is -1/2.

Links

Table of n, a(n) for n=0..100.

Formula

Equals Sum_{k>=0} (-1)^k * bernoulli(2*k)/(2*k)! = Sum_{k>=0} (-1)^k * A027641(2*k)/(A027642(2*k)*(2*k)!). - Amiram Eldar, Jul 22 2020

Example

0.915243860856225...

Mathematica

RealDigits[N[1/(2 Tan[1/2]), 101]]

Prog

(PARI) 1/(2*tan(1/2)) \\ Michel Marcus, Jul 22 2020

Crossrefs

Cf. A027641, A027642.

Sequence in context: A328112 A328097 A197684 * A100924 A350885 A258268

Adjacent sequences: A121221 A121222 A121223 * A121225 A121226 A121227

Keyword

cons,nonn

Author

Fredrik Johansson, Aug 20 2006

Status

approved