A343062 - OEIS

%I #26 Mar 11 2023 07:56:24

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

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

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

%N Decimal expansion of tan(Pi/24).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>

%F Equals sqrt( (2-sqrt(2+sqrt(3)))/(2+sqrt(2+sqrt(3))) ).

%F Equals (sqrt(2)-1)*(sqrt(3)-sqrt(2)) = sqrt(2)-sqrt(3)+sqrt(6)-2.

%e 0.13165249758739585347152...

%t RealDigits[Tan[Pi/24], 10, 100][[1]] (* _Amiram Eldar_, Apr 27 2021 *)

%o (PARI) tan(Pi/24)

%o (PARI) sqrt((2-sqrt(2+sqrt(3)))/(2+sqrt(2+sqrt(3))))

%o (PARI) (sqrt(2)-1)*(sqrt(3)-sqrt(2))

%Y Cf. A144982 (cos (Pi/24)).

%K nonn,cons,easy

%O 0,2

%A _Seiichi Manyama_, Apr 04 2021