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%I #22 May 05 2021 13:50:17
%S 2,2,3,4,5,6,8,9,11,12,14,16,18,20,21,23,25,27,29,31,33,35,38,40,42,
%T 44,46,48,51,53,55,57,60,62,65,67,69,72,74,77,79,82,84,87,89,91,94,97,
%U 99,102,104,107,110,112,115,117,120,123,125,128,130,133,136,138,141,144
%N Average of the first n primes rounded down.
%C Closely related to the prime number theorem; a(n) has the asymptotic expression n * log(n) / 2.
%H Harry J. Smith, <a href="/A060620/b060620.txt">Table of n, a(n) for n = 1..1000</a>
%H Romeo Meštrović, <a href="https://arxiv.org/abs/1804.04198">Curious conjectures on the distribution of primes among the sums of the first 2n primes</a>, arXiv:1804.04198 [math.NT], 2018.
%F a(n) = floor(A007504(n) / n).
%e a(5) = floor((2 + 3 + 5 + 7 + 11)/5) = 5.
%t With[{prms=Prime[Range[500]]},Table[Floor[Mean[Take[prms,n]]],{n,70}]] (* _Harvey P. Dale_, Mar 09 2011 *)
%o (PARI) { n=0; s=0; forprime (p=2, prime(1000), s+=p; write("b060620.txt", n++, " ", floor(s/n)); ) } \\ _Harry J. Smith_, Jul 08 2009
%o (PARI) a(n) = sum(k=1, n, prime(k))\n; \\ _Michel Marcus_, Jul 03 2018
%Y Cf. A007504, A090396.
%K nonn,easy
%O 1,1
%A Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 25 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2001
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