Search: id:A065855
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%I A065855
%S A065855 0,0,0,1,1,2,2,3,4,5,5,6,6,7,8,9,9,10,10,11,12,13,13,14,15,16,17,18,18,
%T A065855 19,19,20,21,22,23,24,24,25,26,27,27,28,28,29,30,31,31,32,33,34,35,36,
%U A065855 36,37,38,39,40,41,41,42,42,43,44,45,46,47,47,48,49,50,50,51,51,52,53
%N A065855 Number of composites <= n.
%C A065855 Also number of primes between prime(n) and n. - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), 
               Sep 24 2002
%C A065855 Plot the points (n,a(n)) by, say, appending the line ListPlot[%, PlotJoined 
               -> True] to the Mathematica program. The result is virtually a straight 
               line passing through the origin. For the first thousand points, the 
               slope is approximately = 3/4. (This behavior can be explained by 
               using the prime number theorem.) - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), 
               Sep 24 2002
%H A065855 T. D. Noe, <a href="b065855.txt">Table of n, a(n) for n=1..1000</a>
%F A065855 a(n)=n-A000720(n)-1=A062298(n)-1.
%e A065855 Prime(8) = 19 and there are 3 primes between 8 and 19 (endpoints are 
               excluded), namely 11, 13, 17. Hence a(8) = 3.
%t A065855 (*gives number of primes < n*) f[n_] := Module[{r, i}, r = 0; i = 1; 
               While[Prime[i] < n, i++ ]; i - 1]; (*gives number of primes between 
               m and n with endpoints excluded*) g[m_, n_] := Module[{r}, r = f[m] 
               - f[n]; If[PrimeQ[n], r = r - 1]; r]; Table[g[Prime[n], n], {n, 1, 
               1000}]
%o A065855 (PARI) { for (n=1, 1000, a=n - primepi(n) - 1; write("b065855.txt", n, 
               " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 
               01 2009]
%Y A065855 Cf. A000720, A062298, A002808, A018252.
%Y A065855 Sequence in context: A099249 A050296 A057062 this_sequence A034137 A156351 
               A057561
%Y A065855 Adjacent sequences: A065852 A065853 A065854 this_sequence A065856 A065857 
               A065858
%K A065855 easy,nonn,nice
%O A065855 1,6
%A A065855 Labos E. (labos(AT)ana.sote.hu), Nov 26 2001

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