The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A013916 Numbers k such that the sum of the first k primes is prime. 36
 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 = 41 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 (Python) from sympy import isprime, prime def aupto(lim): s = 0 for k in range(1, lim+1): s += prime(k) if isprime(s): print(k, end=", ") aupto(680) # Michael S. Branicky, Feb 28 2021 CROSSREFS Cf. A007504, A013917, A013918. Sequence in context: A015663 A352393 A057830 * A141113 A324851 A348572 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 31 15:01 EDT 2023. Contains 361668 sequences. (Running on oeis4.)