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A121224 Decimal expansion of 1/(2*tan(1/2)). 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A258268 A143296

Adjacent sequences:  A121221 A121222 A121223 * A121225 A121226 A121227

KEYWORD

cons,nonn

AUTHOR

Fredrik Johansson, Aug 20 2006

STATUS

approved

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Last modified September 26 05:00 EDT 2020. Contains 337346 sequences. (Running on oeis4.)