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A013916
Numbers k such that the sum of the first k primes is prime.
40
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
OFFSET
1,2
LINKS
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
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)
EXTENSIONS
More terms from David W. Wilson
STATUS
approved