A052434 Nearest integer to R(n) - pi(n), where R(x) is the Riemann prime counting function.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0

Offset: 2

Author

Eric W. Weisstein

Keywords

• sign

Comments

The Riemann prime counting function R(n) = Sum_{prime powers p^k <= n} 1/k = A096624(n)/A096625(n). - N. J. A. Sloane, Feb 07 2023

Examples

			a(13) = 0 because R(13) = 5.504 and pi(13) = 6.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..10000
• H. J. Smith, XPCalc - Extra Precision Floating-Point Calculator [Broken link]
• Eric Weisstein's World of Mathematics, Riemann Prime Counting Function

Crossrefs

Cf. A052435, A096624, A096625.

Programs

XPCalc

a=Round(Ri(n)-Pi(n)) - Harry J. Smith, Dec 31 2008

Extensions

Corrected 6 terms, a(2), a(7), a(10), a(13), a(20) and a(48). Each was made 1 larger. Also gave an example for a(13) and a program for computing a(n). - Harry J. Smith, Dec 31 2008