A301274 Denominator of mean of first n primes.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 6, 19, 20, 21, 22, 1, 8, 5, 26, 27, 28, 29, 10, 31, 32, 33, 34, 35, 12, 37, 38, 39, 40, 41, 14, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 1, 18, 55, 8, 19, 58, 59, 60, 61, 62, 9, 64, 65, 66, 67, 68, 69

Offset

1,2

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.

Example

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, ...

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_] := Mean[Prime[Range[n]]] // Denominator;
a /@ Range[100] (* Jean-François Alcover, Oct 27 2019 *)

Prog

(Python)
from fractions import Fraction
from sympy import prime
A301274_list, mu = [], Fraction(0)
for i in range(1, 10001):
    mu += (prime(i)-mu)/i
    A301274_list.append(mu.denominator) # Chai Wah Wu, Mar 22 2018

Crossrefs

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

Sequence in context: A387050 A080684 A159062 * A093616 A331172 A089247

Adjacent sequences: A301271 A301272 A301273 * A301275 A301276 A301277

Keyword

nonn,frac

Author

N. J. A. Sloane, Mar 18 2018

Status

approved