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A306324 Decimal expansion of 2*Pi*tanh(sqrt(5/3)*Pi/2)/sqrt(15).

%I A306324 #10 Feb 16 2025 08:33:55
%S A306324 1,5,6,7,0,6,5,1,3,1,2,6,4,0,5,4,6,7,7,5,8,8,1,1,1,5,7,7,9,5,9,9,5,4,
%T A306324 6,4,3,9,9,5,1,6,0,0,7,3,4,7,7,6,0,2,3,0,7,4,5,4,1,2,4,3,9,8,3,1,8,4,
%U A306324 1,0,2,0,7,0,4,1,9,8,7,6,2,5,1,5,7,4,8,4,0,6,7,0,0,3,8,0,8,3,6,1,7,7,6,9,3,0,7,6,4,0,1,3,6,2,7,6,7,9,7,9
%N A306324 Decimal expansion of 2*Pi*tanh(sqrt(5/3)*Pi/2)/sqrt(15).
%C A306324 Decimal expansion of the sum of the reciprocals of the centered triangular numbers (A005448).
%H A306324 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%F A306324 Equals Sum_{k>=1} 1/(3*k*(k - 1)/2 + 1).
%F A306324 Equals Sum_{k>=1} 1/A005448(k).
%e A306324 1.56706513126405467758811157795995464399516007...
%t A306324 RealDigits[2 Pi Tanh[Sqrt[5/3] Pi/2]/Sqrt[15], 10, 120][[1]]
%o A306324 (PARI) 2*Pi*tanh(sqrt(5/3)*Pi/2)/sqrt(15) \\ _Michel Marcus_, Feb 08 2019
%Y A306324 Cf. A005448, A226985, A228048 (decimal expansion of the sum of the reciprocals of the centered square numbers), A303658.
%K A306324 nonn,cons
%O A306324 1,2
%A A306324 _Ilya Gutkovskiy_, Feb 07 2019