|
| |
|
|
A057752
|
|
Difference between Li(10^n) and Pi(10^n), where Li(x) = integral of log(x) and Pi(x) = number of primes <= x (A006880).
|
|
4
| |
|
|
2, 5, 10, 17, 38, 130, 339, 754, 1701, 3104, 11588, 38263, 108971, 314890, 1052619, 3214632, 7956589, 21949555, 99877775, 222744644, 597394254, 1932355208
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| On his prime pages C. K. Caldwell remarks: "However in 1914 Littlewood proved that pi(x)-Li(x) assumes both positive and negative values infinitely often". - Frank Ellermann, May 31, 2003
|
|
|
REFERENCES
| John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint of Springer-Verlag, NY, 1995, page 146.
Anatolii A. Karatsuba and Ekatherina A. Karatsuba, The "problem of remainders" in theoretical physics: "physical zeta" function, http://www.phy.bg.ac.rs/~mphys6/proceedings5/14-KaratsubaKaratsuba.ps.
|
|
|
LINKS
| Chris K. Caldwell, How many primes are there, table, Values of pi(x).
Chris K. Caldwell, How many primes are there, table, Approximations to pi(x).
Xavier Gourdon & Pascal Sebah, Counting the primes
Andrew Granville, Harald Cramer and the Distribution of Prime Numbers
Tomas Oliveira e Silva, Tables of values of pi(x) and of pi2(x)
Y. Saouter, P. Demichel, A sharp region where pi(x)-li(x) is positive, Math. Comp. 79 (272) (2010) 2395-2405. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 08 2010]
Munibah Tahir, A new bound for the smallest x with pi(x) > li(x) (2010)
Eric Weisstein's World of Mathematics, Prime Counting Function
Wikipedia, Prime number theorem
|
|
|
MATHEMATICA
| Table[Round[LogIntegral[10^n] - PrimePi[10^n]], {n, 1, 13}]
|
|
|
PROG
| (PARI) A057752=vector(#A006880, i, round(-eint1(-log(10^i))-A006880[i])) - M. F. Hasler (www.univ-ag.fr/~mhasler), Feb 26 2008
|
|
|
CROSSREFS
| Cf. A006880, A052435, A045916, A057794.
Sequence in context: A018315 A146220 A054964 * A173057 A172114 A146010
Adjacent sequences: A057749 A057750 A057751 * A057753 A057754 A057755
|
|
|
KEYWORD
| sign,hard
|
|
|
AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 30 2000
|
|
|
EXTENSIONS
| More terms from Frank Ellermann, May 31, 2003
The value of a(23) is not known at present, I believe. - N. J. A. Sloane (njas(AT)research.att.com), Mar 17 2008
|
| |
|
|
