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 A013916 Numbers k such that the sum of the first k primes is prime. 35
 1, 2, 4, 6, 12, 14, 60, 64, 96, 100, 102, 108, 114, 122, 124, 130, 132, 146, 152, 158, 162, 178, 192, 198, 204, 206, 208, 214, 216, 296, 308, 326, 328, 330, 332, 334, 342, 350, 356, 358, 426, 446, 458, 460, 464, 480, 484, 488, 512, 530, 536, 548, 568, 620, 630, 676, 680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS David W. Wilson, Table of n, a(n) for n = 1..10000 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) = A000720(A013917(n)). EXAMPLE 6 is a term because the sum of the first six primes 2 + 3 + 5 + 7 + 11 + 13 = 31 is prime. MAPLE p:=proc(n) if isprime(sum(ithprime(k), k=1..n))=true then n else fi end: seq(p(n), n=1..690); # Emeric Deutsch MATHEMATICA s = 0; Do[s = s + Prime[n]; If[PrimeQ[s], Print[n]], {n, 1, 1000}] Flatten[Position[Accumulate[Prime[Range[2000]]], _?(PrimeQ[#] &)]] (* Harvey P. Dale, Dec 16 2010 *) Flatten[Position[PrimeQ[Accumulate[Prime[Range[2000]]]], True]] (* Fred Patrick Doty, Aug 15 2017 *) PROG (PARI) isA013916(n) = isprime(sum(i=1, n, prime(i))) \\ Michael B. Porter, Jan 29 2010 (MAGMA) [n:n in [1..700] | IsPrime(&+PrimesUpTo(NthPrime(n))) ]; // Marius A. Burtea, Jan 04 2019 (MATLAB) p=primes(10000); m=1; for u=1:700 ; suma=sum(p(1:u));      if isprime(suma)==1 ; sol(m)=u; m=m+1; end end sol; % Marius A. Burtea, Jan 04 2019 (GAP) P:=Filtered([1..5300], IsPrime);; a:=Filtered([1..Length(P)], n->IsPrime(Sum([1..n], k->P[k])));; Print(a); # Muniru A Asiru, Jan 04 2019 CROSSREFS Cf. A007504, A013917, A013918. Sequence in context: A015636 A015663 A057830 * A141113 A324851 A255001 Adjacent sequences:  A013913 A013914 A013915 * A013917 A013918 A013919 KEYWORD nonn,nice 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 October 14 03:58 EDT 2019. Contains 327995 sequences. (Running on oeis4.)