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A075465 Rounded average of first n primes.

%I A075465 #34 Oct 03 2015 09:09:34
%S A075465 2,2,3,4,6,7,8,10,11,13,15,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
%T A075465 45,47,49,51,53,55,58,60,63,65,67,70,72,75,77,80,82,85,87,90,92,94,97,
%U A075465 100,102,105,107,110,113,115,118,121,123,126,128,131,133,136
%N A075465 Rounded average of first n primes.
%C A075465 38 is an average of first n=23 primes; 110 (n=53); 3066 (n=853); 60020(n=11869). For other n, an average of first n primes is non-integer, in general the function "mean prime(n)" may be non-monotonic, in places of large gaps between primes.
%C A075465 In case of a tie, round down. Thus a(2) = 2, not 3. The next cases where this arises are a(1810) = 7265 and a(2458) = 10285. - _Robert Israel_, Oct 02 2015
%H A075465 Robert Israel, <a href="/A075465/b075465.txt">Table of n, a(n) for n = 1..10000</a>
%F A075465 a(n) = round(A007504(n) / n). - _Ran Pan_, Oct 02 2015
%F A075465 a(n) ~ n * log(n) / 2. - _Ran Pan_, Oct 02 2015
%e A075465 38 is an average of first n=23 primes; 110 (n=53);
%p A075465 rd:= t -> ceil(t+1/2)-1:
%p A075465 Primes:= select(isprime, [2,seq(2*i+1,i=1..1000)]):
%p A075465 S:= ListTools:-PartialSums(Primes):
%p A075465 zip((a,b) -> rd(a/b), S, [$1..nops(S)]); # _Robert Israel_, Oct 02 2015
%t A075465 rnd[n_]:=Block[{ip=IntegerPart[n]},If[n>ip+1/2,ip+1,ip]]; r=Range@1000;rnd@#&/@(Accumulate[Prime[r]]/r) (* Robert G. Wilson v Oct 02 2015 *)
%Y A075465 Cf. A007504, A060620.
%K A075465 easy,nonn
%O A075465 1,1
%A A075465 _Zak Seidov_, Oct 11 2002