A363477 Numbers that are integer averages of first k odd primes for some k.

3, 4, 5, 133, 169, 1117, 2406, 3564, 6141, 7429, 8220, 8475, 14193, 33543, 121049, 211785, 877650, 5948070, 8494543, 27820975, 41428418, 130490020, 139053727, 200325407, 291720414, 893706168, 977748014, 2103851425, 2173904606, 5996888467, 15790305181

Offset: 1

Author

Ya-Ping Lu, Jun 07 2023

Keywords

• nonn

Examples

			5 is a term because 5 is the average of the first 3 odd primes, 3, 5 and 7.
133 is a term because 133 is the average of the first 60 odd primes, 3, 5, 7, 11, ..., 281 and 283.
		

Crossrefs

Cf. A050248, A071148, A097961.

Programs

Python

from sympy import sieve
L = sieve.primerange(3, 4*10**10); s, k = 0, 0
for p in L:
    s += p;  k += 1
    if s%k == 0: print(s//k, end = ", ")

Formula

a(n) = Sum_{i=1..A097961(n)} prime(i)/n.