A301277 Nearest integer to mean of first n primes.

2, 3, 3, 4, 6, 7, 8, 10, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 45, 47, 49, 51, 53, 55, 58, 60, 63, 65, 67, 70, 72, 75, 77, 80, 82, 85, 87, 90, 92, 94, 97, 100, 102, 105, 107, 110, 113, 115, 118, 121, 123, 126, 128, 131, 133

Offset: 1

Author

N. J. A. Sloane, Mar 18 2018

Keywords

• nonn

Comments

Differs from A075465 where ties are involved. - R. J. Mathar, Mar 20 2018

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

• Altug Alkan, 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.

Cf. A007504, A060620, A062049, A075465, A225804, A250130/A024451.

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

Rest@ FoldList[{Append[First@ #1, #2], If[And[EvenQ@ #1, #2 == 1/2] & @@ {IntegerPart@ #, FractionalPart@ #}, Round@ # + 1, Round@ #] &@ Mean@ First@ #1} &, {{2}, 2}, Prime@ Range[2, 63]][[All, -1]] (* Michael De Vlieger, Apr 05 2018 *)

PARI

a(n) = round(sum(i=1, n, prime(i))/n); \\ Altug Alkan, Mar 22 2018

Formula

a(n) = round(A007504(n) / n). - David A. Corneth, Mar 22 2018

a(n) ~ prime(n)/2 ~ n*log(n)/2. - Daniel Forgues, Mar 22 2018