%I
%S 23,41,109,187,349,551,841,1079,1667,1779,2357,2599,3219,3487,3631,
%T 4319,4533,5197,5501,6213,7039,8709,9031,9829,11233,12425,13227,13677,
%U 14329,14813,18667,18951,19073,19973,20561,24329,24685,25153,25561,26261
%N Sums of pth to the qth prime where p and q are twin primes.
%C Conjecture: The number of terms in this sequence is infinite.
%H Danny Rorabaugh, <a href="/A114379/b114379.txt">Table of n, a(n) for n = 1..10000</a>
%F prime(k) = A000040(k) is the kth prime number.
%F a(n) = Sum_{k=A077800(2n1)..A077800(2n)} prime(k).  _Danny Rorabaugh_, Apr 01 2015
%e 3 and 5 are the first twin prime pair: prime(3) = 5, prime(4) = 7, prime(5) = 11
%e and 5+7+11 = 23, the first entry in the table.
%t Plus @@ (Prime /@ Range[#, # + 2]) & /@ Select[Prime@ Range@ 200, PrimeQ[# + 2] &] (* _Michael De Vlieger_, Apr 01 2015 *)
%o (PARI) sumprimes(m, n) = { local(x); return(sum(x=m, n, prime(x))) }
%o g(n)=forprime(x=3,n,if(isprime(x+2),print1(sumprimes(x,x+2)",")))
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Feb 10 2006
