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A013916
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Numbers k such that the sum of the first k primes is prime.
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36
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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
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OFFSET
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1,2
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LINKS
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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.
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FORMULA
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a(n) = A000720(A013917(n)).
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EXAMPLE
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6 is a term because the sum of the first six primes 2 + 3 + 5 + 7 + 11 + 13 = 41 is prime.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A007504, A013917, A013918.
Sequence in context: A015636 A015663 A057830 * A141113 A324851 A334156
Adjacent sequences: A013913 A013914 A013915 * A013917 A013918 A013919
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)
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EXTENSIONS
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More terms from David W. Wilson
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STATUS
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approved
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