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

2,108

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

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

Example

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

Prog

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

Crossrefs

Cf. A052435, A096624, A096625.

Sequence in context: A379678 A104124 A347246 * A369034 A015241 A253513

Adjacent sequences: A052431 A052432 A052433 * A052435 A052436 A052437

Keyword

sign

Author

Eric W. Weisstein

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

Status

approved