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%I #11 Mar 27 2023 23:54:30
%S 1,7,8,4,5,5,9,9,5,4,0,4,1,0,8,6,0,8,1,6,8,2,6,3,3,8,4,1,2,5,1,9,0,9,
%T 7,0,3,5,6,9,3,2,8,7,4,3,3,6,9,6,4,5,2,3,9,2,1,1,8,1,1,4,8,5,9,4,8,1,
%U 6,8,7,0,0,9,2,0,1,6,0,9,5,2,1,1,7,5,1,3,4,0,4,0,8,4,8,8,2,0,8,6,7,6
%N Decimal expansion of 0th Gram point.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GramPoint.html">Gram Point</a>
%e 17.8455995...
%t First[ RealDigits[t /. FindRoot[ RiemannSiegelTheta[t] == 0, {t, 17}, WorkingPrecision -> 120], 10, 102]] (* _Jean-François Alcover_, Jun 07 2012 *)
%o (PARI) g0(n)=2*Pi*exp(1+lambertw((8*n+1)/exp(1)/8)) \\ approximate location of gram(n)
%o th(t)=arg(gamma(1/4+I*t/2))-log(Pi)*t/2 \\ theta, but off by some integer multiple of 2*Pi
%o thapprox(t)=log(t/2/Pi)*t/2-t/2-Pi/8+1/48/t-1/5760/t^3
%o RStheta(t)=my(T=th(t)); (thapprox(t)-T)\/(2*Pi)*2*Pi+T
%o gram(n)=my(G=g0(n),k=n*Pi); solve(x=G-.003,G+1e-8,RStheta(x)-k)
%o gram(0) \\ _Charles R Greathouse IV_, Jan 22 2022
%o (PARI) solve(t=17.8,18,4*Pi+arg(gamma(1/4+I*t/2))-log(Pi)*t/2) \\ _Charles R Greathouse IV_, Mar 27 2023
%Y Cf. A114856, A114858.
%K nonn,cons
%O 2,2
%A _Eric W. Weisstein_, Jan 02 2006
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