|
%I #11 Jul 29 2017 21:25:09
%S 2,2,3,5,11,23,29,31,53,67,79,89,97,107,149,163,223,229,241,271,277,
%T 283,307,313,347,353,373,379,401,433,443,449,479,521,541,547,557,571,
%U 601,631,659,673,683,769,797,811,821,839,853,857,881,907,953,971,1033,1051
%N Primes in A060620, i.e., primes which are integer parts of averages of initial primes.
%C The sum of the reciprocals of the averages and integer parts of the averages both appear to converge. The difference between the two converges to 0.15971929...
%F a(n) = floor((Sum_{x=1..k} prime(x))/k) where k = 1, 2, ... prime(k) <= n.
%e 11 is in the sequence since the average of the first 10 primes is floor((2+3+5+7+11+13+17+19+23+29)/10) = floor(119/10) = 11.
%o (PARI) \ moving average of the primes movavgp(p) = { ct=s=sr1=sr2=0; forprime(x=2,p, ct++; s+=x; y = floor(s/ct +.0); if(isprime(y), sr1+=1.0/y; sr2+=1.0/(s/ct); print1(y" "); ); ); print(); print(sr1" "sr2); print(); print(sr1-sr2); }
%Y Cf. A060620.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Dec 31 2002
%E Edited by _Henry Bottomley_, Jan 02 2003
|
