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Decimal expansion of (3/13)*sqrt(3).
3

%I #10 Jul 17 2024 19:04:46

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

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

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

%N Decimal expansion of (3/13)*sqrt(3).

%F Equals Sum_{k>=0} tan(k*Pi/3)/3^k.

%e 0.39970403251589476004479530957827823852526275087931860...

%t s = Sum[Tan[k Pi/3]/3^k, {k, 0, Infinity}]

%t d = N[s, 100]

%t First[RealDigits[d]]

%t N[(3 Sqrt[3])/13, 100]

%t RealDigits[(3*Sqrt[3])/13,10,120][[1]] (* _Harvey P. Dale_, Jul 17 2024 *)

%o (Python)

%o from math import isqrt

%o def A372914(n): return isqrt(27*10**(n+1<<1)//169)%10 # _Chai Wah Wu_, Jul 08 2024

%Y Cf. A372912, A372913.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 01 2024