Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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