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

1,1

Links

Table of n, a(n) for n=1..31.

Formula

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

Example

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.

Prog

(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 = ", ")

Crossrefs

Cf. A050248, A071148, A097961.

Sequence in context: A085841 A163483 A327876 * A004784 A338056 A321404

Adjacent sequences: A363474 A363475 A363476 * A363478 A363479 A363480

Keyword

nonn

Author

Ya-Ping Lu, Jun 07 2023

Status

approved