A225804 - OEIS

%I #18 Apr 03 2023 10:36:13

%S 2,3,4,5,6,7,9,10,12,13,15,17,19,21,22,24,26,28,30,32,34,36,38,41,43,

%T 45,47,49,52,54,56,58,61,63,66,68,70,73,75,78,80,83,85,88,90,92,95,98,

%U 100,103,105,108,110,113,116,118,121,124

%N Arithmetic mean of the first n primes, rounded up.

%H K. D. Bajpai, <a href="/A225804/b225804.txt">Table of n, a(n) for n = 1..5000</a>

%H Chris K. Caldwell and G. L. Honaker,Jr.,<a href="https://t5k.org/curios/page.php?short=110"> Prime Curios! 110</a>

%F a(n) = ceiling(A007504(n) / n)

%e a(5) = ceiling( (2 + 3 + 5 + 7 + 11)/5) = ceiling(28/5) = 6.

%e a(6) = ceiling( (2 + 3 + 5 + 7 + 11 + 13)/6) = ceiling(41/6) = 7.

%e a(7) = ceiling( (2 + 3 + 5 + 7 + 11 + 13 + 17)/7) = ceiling(58/7) = 9.

%p A007504 := proc(n)

%p     add(ithprime(i),i=1..n) ;

%p end proc:

%p A225804 := proc(n)

%p     ceil(A007504(n)/n) ;

%p end proc: # _R. J. Mathar_, Jul 28 2013

%t Table[Ceiling[(Plus@@Prime[Range[n]])/n], {n, 75}] (* _Alonso del Arte_, Jul 28 2013 *)

%Y Cf. A007504, A060620 (rounded down).

%K nonn,easy

%O 1,1

%A _K. D. Bajpai_, Jul 28 2013