This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A135544 #10 Jan 23 2025 22:18:25
%S A135544 0,0,0,0,5,1,7,2,3,1,8,6,2,0,3,8,1,2,3,0,6,1,4,5,4,6,5,0,9,0,3,8,2,3,
%T A135544 9,3,6,9,5,5,7,8,7,6,9,6,9,8,3,6,6,8,0,8,9,4,1,4,2,7,6,5,8,8,1,8,4,7,
%U A135544 1,6,8,3,1,5,1,0,3,2,3,0,5,6,7,6,2,0,6,8,5,5,9,8,1,9,5,3,1,9,3,3,3
%N A135544 Decimal expansion of (-1)^(I Pi).
%H A135544 G. C. Greubel, <a href="/A135544/b135544.txt">Table of n, a(n) for n = 0..2500</a>
%H A135544 Doctor Bombelli, The Math Forum, <a href="http://mathforum.org/library/drmath/view/53907.html">Exp[ -I * Pi] = Cos[Pi] + i Sin[Pi] = -1</a>.
%F A135544 a(n) = (-1)^(I Pi) = exp(-Pi)^Pi = (exp( -(1/2)*Pi))^(2*Pi) = sqrt(exp( -Pi)^Pi/(exp(Pi)^Pi)) = exp[(-1/2*Pi)]^(Gamma[1/6]*Gamma[5/6]) = 1/(sqrt[exp[Pi]^(2*Pi)]) = (exp[ -(1/2)*Pi])^(2*Pi) = exp[ -Pi^2].
%e A135544 (-1)^(I*Pi) = exp(-Pi)^(Pi) = 0.000051723186...
%t A135544 N[(-1)^(I Pi), 1000] FullSimplify[(-1)^(I Pi) == Exp[ -Pi]^Pi == (Exp[ -(1/2)*Pi])^(2*Pi) == Sqrt[Exp[ -Pi]^Pi/(Exp[Pi]^Pi)] == Exp[(-1/2*Pi)]^(Gamma[1/6]*Gamma[5/6]) == 1/(Sqrt[Exp[Pi]^(2*Pi)]) == (Exp[ -(1/2)*Pi])^(2*Pi) == Exp[ -Pi^2]]
%t A135544 Join[{0, 0, 0, 0}, RealDigits[(Exp[-Pi])^(Pi), 10, 96][[1]]] (* _G. C. Greubel_, Oct 18 2016 *)
%o A135544 (PARI) exp(-Pi^2) \\ _Charles R Greathouse IV_, Jan 23 2025
%o A135544 (PARI) real((-1)^(I*Pi)) \\ _Charles R Greathouse IV_, Jan 23 2025
%Y A135544 Cf. A057521, A002388, A093580.
%K A135544 nonn,cons
%O A135544 0,5
%A A135544 _Marvin Ray Burns_, Feb 22 2008, Feb 23 2008
%E A135544 Offset corrected _R. J. Mathar_, Jan 26 2009