A053790 Composite numbers arising as sum of first k primes.

10, 28, 58, 77, 100, 129, 160, 238, 328, 381, 440, 501, 568, 639, 712, 791, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 1988, 2127, 2276, 2427, 2584, 2747, 2914, 3087, 3266, 3447, 3638, 3831, 4028, 4227, 4438, 4661, 4888, 5117, 5350, 5589, 5830

Offset: 1

Author

Enoch Haga, Mar 27 2000

Keywords

• easy
• nonn

Comments

Generate sum of first k primes; accept if not prime.

Examples

			a(4) = 77 because 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 = A007504(8) is composite, and 77 is the 4th such composite sum of k primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053789, A013918, A066527.

Intersection of A002808 and A007504.

Programs

Maple

N:= 10^4: # to use primes <= N
P:= select(isprime,[2,seq(i,i=3..N,2)]):
remove(isprime,ListTools:-PartialSums(P)); # Robert Israel, Sep 22 2016

Mathematica

Cases[Accumulate[Prime[Range[100]]],Except[?PrimeQ]] (*_Fred Patrick Doty Aug 22 2017*)

PARI

first(n)=my(v=vector(n),s,i); forprime(p=2,, if(isprime(s+=p), next); v[i++]=s; if(i==n, break)); v \\ Charles R Greathouse IV, Aug 23 2017

Python

from sympy import isprime, nextprime
def aupto(limit):
    alst, s, p = [], 2, 2
    while s < limit:
        if not isprime(s): alst.append(s)
        p = nextprime(p)
        s += p
    return alst
print(aupto(6000)) # Michael S. Branicky, Oct 28 2021

Formula

{k: A007504(k) in A002808}. - Michael S. Branicky, Oct 28 2021