A263076 Numbers n such that the fractional part of the sum of the first n primes (A007504) divided by n equals 1/2.

2, 1810, 2458, 240926, 317602, 757730, 771610, 23993994, 58292586, 172616042

Offset: 1

Author

Robert G. Wilson v, Oct 09 2015

Keywords

• nonn
• more
• hard

Comments

Inspired by A075465.

No other terms < 10^9.

All terms are even. - Charles R Greathouse IV, Oct 09 2015

Examples

			a(1) = 2 since A007504(2) = 5 and 5/2 has a remainder of half of 2 which is 1.
a(2) = 1810 because A007504(1810) = 13150555 and 13150555/1810 = 14531/2.
		

Crossrefs

Cf. A007504, A045345, A075465.

Programs

Mathematica

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++]

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