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Smallest prime that is the sum of prime(n) consecutive primes.
0

%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