A267087 - OEIS

%I #17 Jan 24 2016 22:57:26

%S 4,5,7,9,11,13,17,19,23,25,29,33,37,41,43,47,51,55,59,63,67,71,76,81,

%T 85,89,93,97,103,107,111,115,121,125,131,135,139,145,149,155,159,165,

%U 169,175,179,183,189,195,199,205,209,215,220,225,231,235,241

%N a(n) = ceiling(A007504(n)/n) + floor(A007504(n)/n).

%C Primes not in this sequence 2, 3, 31, 53, 61, 73, 79, 83, 101, 109, 113, 127, 137, 151,...

%C a(n) is even for n=1, 23, 53, 853, ... see A045345.

%C It appears that there are infinitely many even terms in this sequence but that they have density zero.

%D Javier Cilleruelo and Florian Luca, On the sum of the first n primes, Q. J. Math. 59:4 (2008), 14 pp.

%t Table[Ceiling[(Plus@@Prime[Range[n]])/n]+Floor[(Plus@@Prime[Range[n]])/n], {n, 100}]

%Y Cf. A007504, A045345, A060620, A158682, A225804, A267084.

%K nonn,easy

%O 1,1

%A _Ctibor O. Zizka_, Jan 10 2016