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A160327 Decimal expansion of (e-1)/(e+1).

%I A160327 #27 Jan 03 2023 10:16:10
%S A160327 4,6,2,1,1,7,1,5,7,2,6,0,0,0,9,7,5,8,5,0,2,3,1,8,4,8,3,6,4,3,6,7,2,5,
%T A160327 4,8,7,3,0,2,8,9,2,8,0,3,3,0,1,1,3,0,3,8,5,5,2,7,3,1,8,1,5,8,3,8,0,8,
%U A160327 0,9,0,6,1,4,0,4,0,9,2,7,8,7,7,4,9,4,9,0,6,4,1,5,1,9,6,2,4,9,0,5,8,4,3,4,8
%N A160327 Decimal expansion of (e-1)/(e+1).
%H A160327 Harry J. Smith, <a href="/A160327/b160327.txt">Table of n, a(n) for n = 0..20000</a>
%H A160327 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A160327 (e-1)/(e+1) = tanh(1/2).
%F A160327 Equals 2 * Sum_{k>=1} (2^(2*k)-1)*B(2*k)/(2*k)!, where B(2*k) = A000367(k)/A002445(k) are the Bernoulli numbers. - _Amiram Eldar_, Nov 25 2020
%F A160327 Equals -i * tan(i/2). - _Michal Paulovic_, Jan 03 2023
%e A160327 0.462117157260009758502318483643672548730289280330113038552731815838080...
%t A160327 RealDigits[(E-1)/(E+1), 10, 100][[1]] (* _G. C. Greubel_, Oct 05 2018 *)
%o A160327 (PARI) default(realprecision, 20080); x=tanh(1/2)*10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b160327.txt", n, " ", d));
%o A160327 (PARI) (exp(1)-1)/(exp(1)+1) \\ _Altug Alkan_, Oct 05 2018
%o A160327 (Magma) SetDefaultRealField(RealField(100)); (Exp(1) - 1)/(Exp(1) + 1); // _G. C. Greubel_, Oct 05 2018
%Y A160327 Cf. A016825 (continued fraction), A086403/A079165 (convergents).
%Y A160327 Cf. A000367, A002445.
%K A160327 nonn,easy,cons
%O A160327 0,1
%A A160327 _Harry J. Smith_, May 09 2009