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Sum of primes <= p is even and sum is twice a prime.
1

%I #14 Nov 22 2016 18:32:07

%S 5,17,257,277,313,379,487,751,773,811,1579,1787,2081,2467,2557,2671,

%T 2689,3037,3343,3559,4091,4159,4373,4451,4567,4793,5039,5441,6037,

%U 6113,6131,6269,6337,6547,6719,6829,7193,7351,7547,7649,8039,8059,9239,9859

%N Sum of primes <= p is even and sum is twice a prime.

%H Harvey P. Dale, <a href="/A089894/b089894.txt">Table of n, a(n) for n = 0..1000</a>

%e 17 is in the sequence because 2+3+5+7+11+13+17 = 58 and 58 = 2 * 29 and 29 is prime.

%t Prime[#]&/@Flatten[Position[Accumulate[Prime[Range[1300]]],_?(EvenQ[#] && PrimeQ[#/2]&)]] (* _Harvey P. Dale_, Oct 04 2012 *)

%o (PARI) s=2; forprime(p=3,15000,s=s+p;if(s%2,i=1,if(isprime(s/2),print1(p,", "),)))

%K easy,nonn

%O 0,1

%A _Randy L. Ekl_, Jan 10, 2004