OFFSET
1,1
COMMENTS
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...
FORMULA
a(n) = floor((Sum_{x=1..k} prime(x))/k) where k = 1, 2, ... prime(k) <= n.
EXAMPLE
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.
PROG
(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); }
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 31 2002
EXTENSIONS
Edited by Henry Bottomley, Jan 02 2003
STATUS
approved