A053790 - OEIS

%I #21 Oct 28 2021 09:59:18

%S 10,28,58,77,100,129,160,238,328,381,440,501,568,639,712,791,874,963,

%T 1060,1161,1264,1371,1480,1593,1720,1851,1988,2127,2276,2427,2584,

%U 2747,2914,3087,3266,3447,3638,3831,4028,4227,4438,4661,4888,5117,5350,5589,5830

%N Composite numbers arising as sum of first k primes.

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

%H Robert Israel, <a href="/A053790/b053790.txt">Table of n, a(n) for n = 1..10000</a>

%F {k: A007504(k) in A002808}. - _Michael S. Branicky_, Oct 28 2021

%e 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.

%p N:= 10^4: # to use primes <= N

%p P:= select(isprime,[2,seq(i,i=3..N,2)]):

%p remove(isprime,ListTools:-PartialSums(P)); # _Robert Israel_, Sep 22 2016

%t Cases[Accumulate[Prime[Range[100]]],Except[_?PrimeQ]] (*_Fred Patrick Doty_ Aug 22 2017*)

%o (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

%o (Python)

%o from sympy import isprime, nextprime

%o def aupto(limit):

%o     alst, s, p = [], 2, 2

%o     while s < limit:

%o         if not isprime(s): alst.append(s)

%o         p = nextprime(p)

%o         s += p

%o     return alst

%o print(aupto(6000)) # _Michael S. Branicky_, Oct 28 2021

%Y Cf. A053789, A013918, A066527.

%Y Intersection of A002808 and A007504.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Mar 27 2000