A013918 Primes equal to the sum of the first k primes for some k.

2, 5, 17, 41, 197, 281, 7699, 8893, 22039, 24133, 25237, 28697, 32353, 37561, 38921, 43201, 44683, 55837, 61027, 66463, 70241, 86453, 102001, 109147, 116533, 119069, 121631, 129419, 132059, 263171, 287137, 325019, 329401, 333821, 338279, 342761

Offset

1,1

Comments

Intersection of A000040 and A007504. - David W. Wilson, May 11 2007

Sum of the first k primes p_1+p_2+...+p_k is in the sequence if and only if there exists the prime q for which p_i divides p_1+p_2+...+p_k+q for all i to k. - Vladimir Letsko, Oct 13 2013

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Vladimir Letsko, Mathematical Marathon, problem 124 (in Russian).

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) = A007504(A013916(n)).

Mathematica

Select[Accumulate[Prime[Range[1000]]], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)

Prog

(PARI) n=0; forprime(k=2, 2300, n=n+k; if(isprime(n), print(n))) \\ Michael B. Porter, Jan 29 2010
(Haskell)
a013918 n = a013918_list !! (n-1)
a013918_list = filter ((== 1) . a010051) a007504_list
-- Reinhard Zumkeller, Feb 09 2015

Crossrefs

Cf. A013916, A013917, A189153 (number of these primes < 10^n).

Cf. A007504, A010051, A000040.

Sequence in context: A080898 A346134 A081763 * A007351 A300692 A076076

Adjacent sequences: A013915 A013916 A013917 * A013919 A013920 A013921

Keyword

nonn

Author

N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)

Extensions

More terms from David W. Wilson

Status

approved