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 A078445 Primes in A060620, i.e., primes which are integer parts of averages of initial primes. 2
 2, 2, 3, 5, 11, 23, 29, 31, 53, 67, 79, 89, 97, 107, 149, 163, 223, 229, 241, 271, 277, 283, 307, 313, 347, 353, 373, 379, 401, 433, 443, 449, 479, 521, 541, 547, 557, 571, 601, 631, 659, 673, 683, 769, 797, 811, 821, 839, 853, 857, 881, 907, 953, 971, 1033, 1051 (list; graph; refs; listen; history; text; internal format)
 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... LINKS 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 Cf. A060620. Sequence in context: A058697 A030427 A049907 * A127166 A103596 A005426 Adjacent sequences:  A078442 A078443 A078444 * A078446 A078447 A078448 KEYWORD easy,nonn AUTHOR Cino Hilliard, Dec 31 2002 EXTENSIONS Edited by Henry Bottomley, Jan 02 2003 STATUS approved

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Last modified June 23 13:39 EDT 2021. Contains 345401 sequences. (Running on oeis4.)