A096623 Decimal expansion of Integral_{t>=2} 1/(t*log(t)(t^2-1)) dt.

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, 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, 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

Offset: 0

Author

Eric W. Weisstein, Jul 01 2004

Keywords

• nonn
• cons

Comments

Maximum value of the integral in the Riemann prime counting function.

Examples

			0.1400101011432869266869173052342997331775279281270658289489468743113049149...
		

References

• John Derbyshire, Prime Obsession, Joseph Henry Press, 2003, pp. 328-329.
• Bernhard Riemann, On the Number of Prime Numbers less than a Given Quantity, 1859.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..2509
• Eric Weisstein's World of Mathematics, Riemann Prime Counting Function

Crossrefs

Cf. A096624, A096625.

Programs

Maple

evalf(Integrate(1/(x*log(x)*(x^2-1)), x = 2..infinity), 120); # Vaclav Kotesovec, Feb 13 2019

Mathematica

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 *)

PARI

default(realprecision, 120); intnum(x=2, oo, 1/(x*log(x)*(x^2 - 1))) \\ Vaclav Kotesovec, Feb 13 2019