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%I #46 Feb 08 2024 07:10:57
%S 2,5,17,41,197,281,7699,8893,22039,24133,25237,28697,32353,37561,
%T 38921,43201,44683,55837,61027,66463,70241,86453,102001,109147,116533,
%U 119069,121631,129419,132059,263171,287137,325019,329401,333821,338279,342761
%N Primes equal to the sum of the first k primes for some k.
%C Intersection of A000040 and A007504. - _David W. Wilson_, May 11 2007
%C Sum of the first k primes p_1+p_2+...+p_k is in the sequence if and only if there exists the prime q for which p_i divides p_1+p_2+...+p_k+q for all i to k. - _Vladimir Letsko_, Oct 13 2013
%H T. D. Noe, <a href="/A013918/b013918.txt">Table of n, a(n) for n = 1..10000</a>
%H Vladimir Letsko, <a href="http://dxdy.ru/post354640.html#p354640">Mathematical Marathon, problem 124</a> (in Russian).
%H Romeo Meštrović, <a href="https://arxiv.org/abs/1804.04198">Curious conjectures on the distribution of primes among the sums of the first 2n primes</a>, arXiv:1804.04198 [math.NT], 2018.
%F a(n) = A007504(A013916(n)).
%t Select[Accumulate[Prime[Range[1000]]], PrimeQ] (* _Vladimir Joseph Stephan Orlovsky_, Sep 01 2008 *)
%o (PARI) n=0;forprime(k=2,2300,n=n+k;if(isprime(n),print(n))) \\ _Michael B. Porter_, Jan 29 2010
%o (Haskell)
%o a013918 n = a013918_list !! (n-1)
%o a013918_list = filter ((== 1) . a010051) a007504_list
%o -- _Reinhard Zumkeller_, Feb 09 2015
%Y Cf. A013916, A013917, A189153 (number of these primes < 10^n).
%Y Cf. A007504, A010051, A000040.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Renaud Lifchitz (100637.64(AT)CompuServe.COM)
%E More terms from _David W. Wilson_
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