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%I #46 Oct 01 2013 21:35:21
%S 0,3,10,14,33,39,68,76,92,116,155,185,246,258,282,318,413,427,536,568,
%T 584,632,747,801,873,909,927,963,1090,1130,1397,1441,1507,1529,1639,
%U 1661,1884,1956,2004,2076,2327,2353,2674,2702,2758,2786,3165,3345,3405
%N Prime(n) * pi(n).
%C Pi(n) = number of prime numbers <= n (A000720). Prime(n) = A000040(n).
%C Conjecture: For each n there is at least one prime p such that a(n) < p < a(n+1). From the conjecture follows that the prime gaps g(n) = p(n+1) - p(n) = O(sqrt(p(n))/log(p(n))). Legendre's hypothesis is that g(n) = O(sqrt(p(n))). - _Thomas Ordowski_, Aug 11 2012
%H T. D. Noe, <a href="/A128930/b128930.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Legendre%27s_conjecture">Legendre's conjecture</a>
%F a(n) ~ (n log n)*(n/log n) = n^2. a(n) > n^2 for n > 4. - Thomas Ordowski, Aug 09 2012
%t Table[Prime[n] * PrimePi[n], {n, 50} (* _Harvey P. Dale_, Mar 17 2011 *)
%o (PARI) g(n) = for(x=1,n,y=prime(x)*primepi(x);print1(y","))
%Y Cf. A000040, A000720, A128913.
%K easy,nonn
%O 1,2
%A _Cino Hilliard_, Apr 23 2007
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