A372913 - OEIS

%I #8 Aug 02 2024 09:56:08

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

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

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

%N Decimal expansion of (1/31)*(14*sqrt(5 - 2*sqrt(5)) + 4*sqrt(5 + 2*sqrt(5))).

%F Equals Sum_{k>=0} tan(k*Pi/5)/2^k.

%e 0.72523643679922793589734506157665489647264845405...

%p sqrt(265-62*sqrt(5)) ; %*2/31 ; evalf(%) ; # _R. J. Mathar_, Aug 02 2024

%t s = Sum[Tan[k Pi/5]/2^k, {k, 0, Infinity}]

%t d = N[s, 100]

%t First[RealDigits[d]]

%t N[1/31 (14 Sqrt[5 - 2 Sqrt[5]] + 4 Sqrt[5 + 2 Sqrt[5]]), 100]

%Y Cf. A372912, A372914.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 01 2024