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%I #20 Aug 11 2021 11:00:54
%S 5,23,53,197,233,691,499,857,1151,2099,2399,2909,3821,4217,5107,6079,
%T 10091,8273,12281,11597,12713,15527,22741,26041,25759,37447,28087,
%U 36607,36067,35527,42463,46181,49279,65033,67271,71011,71167,76099,78139,96001,95107
%N Smallest prime that is the sum of prime(n) consecutive primes.
%F Sum of reciprocals converges to 0.28053...
%F a(n) = A070281(prime(n)). - _Michel Marcus_, Aug 07 2021
%e For prime(2) = 3,
%e 2+3+5 = 10,
%e 3+5+7 = 15,
%e 5+7+11 = 23,
%e 7+11+13 = 31.
%e So a(2) = 23, the first prime that is the sum of 3 consecutive primes.
%o (PARI)
%o \\ First prime in the sum of a prime number of consecutive primes
%o upto(n) = { sr=.2; print1(5", "); forprime(i=2,n, s=0; for(j=1,i, s+=prime(j); ); for(x=1,n, s = s - prime(x)+ prime(x+i); if(isprime(s),sr+=1.0/s; print1(s", "); break); ); ); /* print(); print(sr)*/}
%o (Python)
%o from sympy import isprime, nextprime, prime, primerange
%o def a(n):
%o pn = prime(prime(n))
%o smallest = list(primerange(2, pn+1))
%o while not isprime(sum(smallest)):
%o pn = nextprime(pn)
%o smallest = smallest[1:] + [pn]
%o return sum(smallest)
%o print([a(n) for n in range(1, 42)]) # _Michael S. Branicky_, May 23 2021
%Y Cf. A070281.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, May 09 2003
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