Search: id:A057752
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%I A057752
%S A057752 2,5,10,17,38,130,339,754,1701,3104,11588,38263,108971,314890,1052619,
%T A057752 3214632,7956589,21949555,99877775,222744644,597394254,1932355208
%N 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).
%C A057752 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
%D A057752 John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint 
               of Springer-Verlag, NY, 1995, page 146.
%H A057752 Chris K. Caldwell, How many primes are there, table, <a href="http://
               www.utm.edu/research/primes/howmany.shtml#table">Values of pi(x)</
               a>.
%H A057752 Chris K. Caldwell, How many primes are there, table, <a href="http://
               www.utm.edu/research/primes/howmany.shtml#table3">Approximations 
               to pi(x)</a>.
%H A057752 Xavier Gourdon & Pascal Sebah, <a href="http://numbers.computation.free.fr/
               Constants/Primes/countingPrimes.html">Counting the primes</a>
%H A057752 Andrew Granville, <a href="http://www.dartmouth.edu/~chance/chance_news/
               for_chance_news/Riemann/cramer.pdf">Harald Cramer and the Distribution 
               of Prime Numbers</a>
%H A057752 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/primes.html">
               Tables of values of pi(x) and of pi2(x)</a>
%H A057752 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeCountingFunction.html">Prime Counting Function</a>
%H A057752 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_number_theorem">
               Prime number theorem</a>
%t A057752 Table[Round[LogIntegral[10^n] - PrimePi[10^n]], {n, 1, 13}]
%o A057752 (PARI) A057752=vector(#A006880,i,round(-eint1(-log(10^i))-A006880[i])) 
               - M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 26 2008
%Y A057752 Cf. A006880, A052435, A045916, A057794.
%Y A057752 Sequence in context: A018315 A146220 A054964 this_sequence A146010 A077631 
               A025223
%Y A057752 Adjacent sequences: A057749 A057750 A057751 this_sequence A057753 A057754 
               A057755
%K A057752 nonn
%O A057752 1,1
%A A057752 Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 30 2000
%E A057752 More terms from Frank Ellermann, May 31, 2003
%E A057752 The value of a(23) is not known at present, I believe. - N. J. A. Sloane 
               (njas(AT)research.att.com), Mar 17 2008

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