A078445 Primes in A060620, i.e., primes which are integer parts of averages of initial primes.
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
Offset: 1
Examples
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.
Crossrefs
Cf. A060620.
Programs
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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); }
Formula
a(n) = floor((Sum_{x=1..k} prime(x))/k) where k = 1, 2, ... prime(k) <= n.
Extensions
Edited by Henry Bottomley, Jan 02 2003
Comments