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%I #15 Oct 23 2015 13:47:34
%S 2,1810,2458,240926,317602,757730,771610,23993994,58292586,172616042
%N Numbers n such that the fractional part of the sum of the first n primes (A007504) divided by n equals 1/2.
%C Inspired by A075465.
%C No other terms < 10^9.
%C All terms are even. - _Charles R Greathouse IV_, Oct 09 2015
%e a(1) = 2 since A007504(2) = 5 and 5/2 has a remainder of half of 2 which is 1.
%e a(2) = 1810 because A007504(1810) = 13150555 and 13150555/1810 = 14531/2.
%t p = 2; k = s = 0; lst = {}; While[k < 100000001, s = s + p; If[ 2Mod[s, ++k] == k, AppendTo[lst, k]; Print[k]]; p = NextPrime@ p; k++]
%o (PARI) n=s=0; forprime(p=2,, s+=p; n++; if(n%2==0 && s%n == n/2, print1(n", "))) \\ _Charles R Greathouse IV_, Oct 09 2015
%Y Cf. A007504, A045345, A075465.
%K nonn,more,hard
%O 1,1
%A _Robert G. Wilson v_, Oct 09 2015
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