A353781 Decimal expansion of log(sin(2)/2) (negated).

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

Offset

0,1

Comments

We have Sum_{n>=0} log(cos(a/2^n)) = log((sin(2*a))/(2*a)) for 0 < a < Pi/2; this is the particular case a = 1.

References

Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.2.j page 283.

Links

Table of n, a(n) for n=0..93.

Formula

Equals Sum_{n>=0} log(cos(1/2^n)).

Example

-0.7882302166551059406604484922728009...

Maple

evalf(sum(ln(cos(1/2^n)), n=0..infinity), 110);

Mathematica

RealDigits[Log[Sin[2]/2], 10, 100][[1]] (* Amiram Eldar, May 08 2022 *)

Prog

(PARI) log(sin(2)/2) \\ Michel Marcus, May 08 2022

Crossrefs

Cf. A049469.

Sequence in context: A094819 A019861 A065470 * A338815 A197810 A085361

Adjacent sequences: A353778 A353779 A353780 * A353782 A353783 A353784

Keyword

nonn,cons

Author

Bernard Schott, May 08 2022

Status

approved