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 A013918 Primes equal to the sum of the first k primes for some k. 39
 2, 5, 17, 41, 197, 281, 7699, 8893, 22039, 24133, 25237, 28697, 32353, 37561, 38921, 43201, 44683, 55837, 61027, 66463, 70241, 86453, 102001, 109147, 116533, 119069, 121631, 129419, 132059, 263171, 287137, 325019, 329401, 333821, 338279, 342761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A000040 and A007504. - David W. Wilson, May 11 2007 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Vladimir Letsko, Mathematical Marathon, problem 124 (in Russian). Romeo Meštrović, Curious conjectures on the distribution of primes among the sums of the first 2n primes, arXiv:1804.04198 [math.NT], 2018. FORMULA a(n) = A007504(A013916(n)) MAPLE P:=proc(n) local i, j; j:=2; for i from 2 by 1 to n do j:=j+ithprime(i); if isprime(j) then print(j); fi; od; end: P(1000); # Paolo P. Lava, May 05 2006 MATHEMATICA Select[Accumulate[Prime[Range[1000]]], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *) PROG (PARI) n=0; forprime(k=2, 2300, n=n+k; if(isprime(n), print(n))) \\ Michael B. Porter, Jan 29 2010 (Haskell) a013918 n = a013918_list !! (n-1) a013918_list = filter ((== 1) . a010051) a007504_list -- Reinhard Zumkeller, Feb 09 2015 CROSSREFS Cf. A013916, A013917, A189153 (number of these primes < 10^n). Cf. A007504, A010051, A000040. Sequence in context: A118500 A080898 A081763 * A007351 A300692 A076076 Adjacent sequences:  A013915 A013916 A013917 * A013919 A013920 A013921 KEYWORD nonn AUTHOR N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM) EXTENSIONS More terms from David W. Wilson STATUS approved

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Last modified August 18 16:13 EDT 2018. Contains 313833 sequences. (Running on oeis4.)