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%I #31 Nov 03 2022 15:25:58
%S 1,4,0,0,1,0,1,0,1,1,4,3,2,8,6,9,2,6,6,8,6,9,1,7,3,0,5,2,3,4,2,9,9,7,
%T 3,3,1,7,7,5,2,7,9,2,8,1,2,7,0,6,5,8,2,8,9,4,8,9,4,6,8,7,4,3,1,1,3,0,
%U 4,9,1,4,9,9,5,1,6,1,3,6,1,0,2,7,6,0,2,6,5,3,2,0,6,4,8,6,6,6,9,6,3,4,3,4,5
%N Decimal expansion of Integral_{t>=2} 1/(t*log(t)(t^2-1)) dt.
%C Maximum value of the integral in the Riemann prime counting function.
%D John Derbyshire, Prime Obsession, Joseph Henry Press, 2003, pp. 328-329.
%D Bernhard Riemann, On the Number of Prime Numbers less than a Given Quantity, 1859.
%H Robert G. Wilson v, <a href="/A096623/b096623.txt">Table of n, a(n) for n = 0..2509</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>
%e 0.1400101011432869266869173052342997331775279281270658289489468743113049149...
%p evalf(Integrate(1/(x*log(x)*(x^2-1)), x = 2..infinity), 120); # _Vaclav Kotesovec_, Feb 13 2019
%t RealDigits[ NIntegrate[1/(t Log[t](t^2 - 1)), {t, 2, Infinity}, MaxRecursion -> 8, AccuracyGoal -> 115, WorkingPrecision -> 128]][[1]] (* _Robert G. Wilson v_, Jul 05 2004 *)
%o (PARI) default(realprecision, 120); intnum(x=2, oo, 1/(x*log(x)*(x^2 - 1))) \\ _Vaclav Kotesovec_, Feb 13 2019
%Y Cf. A096624, A096625.
%K nonn,cons
%O 0,2
%A _Eric W. Weisstein_, Jul 01 2004
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