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A013916 Numbers k such that the sum of the first k primes is prime. 34
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 July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)