A301273 Numerator of mean of first n primes.

2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281, 328, 381, 440, 167, 568, 639, 712, 791, 38, 321, 212, 1161, 1264, 1371, 1480, 531, 1720, 1851, 1988, 2127, 2276, 809, 2584, 2747, 2914, 3087, 3266, 1149, 3638, 3831, 4028, 4227, 4438, 4661

Offset: 1

Author

N. J. A. Sloane, Mar 18 2018

Keywords

• nonn
• frac

Examples

			The means are 2, 5/2, 10/3, 17/4, 28/5, 41/6, 58/7, 77/8, 100/9, 129/10, 160/11, 197/12, 238/13, 281/14, 328/15, 381/16, 440/17, 167/6, 568/19, 639/20, 712/21, 791/22, 38, 321/8, 212/5, ...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Joel E. Cohen, Statistics of Primes (and Probably Twin Primes) Satisfy Taylor’s Law from Ecology, The American Statistician, 70 (2016), 399-404.

Crossrefs

Mean and variance of primes: A301273/A301274, A301275/A301276, A301277, A273462.

Programs

Maple

m := n -> add(ithprime(j),j=1..n)/n;
m1:=[seq(m(n),n=1..100)];
m2:=map(numer,m1); # A301273
m3:=map(denom,m1); # A301274
m4:=map(round,m1); # A301277

Mathematica

a[n_] := Prime @ Range[n] // Mean // Numerator;
a /@ Range[100] (* Jean-François Alcover, Nov 16 2019 *)

Python

from fractions import Fraction
from sympy import prime
A301273_list, mu = [], Fraction(0)
for i in range(1,10001):
    mu += (prime(i)-mu)/i
    A301273_list.append(mu.numerator) # Chai Wah Wu, Mar 22 2018