A350885 - OEIS

%I #20 Jan 21 2022 10:25:25

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

%T 5,5,2,8,5,6,9,7,2,6,5,8,4,6,3,3,4,8,6,5,9,2,8,2,7,8,4,3,2,5,2,7,2,5,

%U 8,4,5,4,0,3,1,2,5,6,2,6,1,7,3,5,6,6,1,7,0,4,5,4,4,2,0,4,6

%N Decimal expansion of 1 - 2*cotan(2).

%C The constant given in the name is computed using a telescopic sum coming from cotan(x) - 2*cotan(2*x) = tan(x).

%D J. Quinet, Cours élémentaire de Mathématiques Supérieures, Tome 3, Calcul intégral et Séries, Bordas, 1973, Exercice 7.36, pp 111 and 231.

%F Equals Sum_{m>=0} (1/2^m) * (tan(1/2^m)).

%F Equals (t^2+t-1)/t with t=A049471. - _Michel Marcus_, Jan 21 2022

%e 1.915315108720571527500554820864094552856972658463348659...

%p evalf(1-2/tan(2),120);

%t RealDigits[1 - 2*Cot[2], 10, 100][[1]] (* _Amiram Eldar_, Jan 21 2022 *)

%o (PARI) 1-2*cotan(2) \\ _Michel Marcus_, Jan 21 2022

%Y Cf. A049471, A073449.

%K nonn,cons

%O 1,2

%A _Bernard Schott_, Jan 21 2022