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

1,1

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

Table of n, a(n) for n=1..56.

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