This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
A070281(13) = 691 = prime(10) + ... + prime(22), thus a(13) = 10.
Every term of the increasing sequence of primes 127, 401, 439, 479, 593,... is splittable into a sum of 9 consecutive odd primes and 127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 is the least one corresponding to n = 4.
f[n_] := Block[{k = 1, s},While[s = Sum[Prime[i], {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[f[n], {n, 0, 41}] (* Ray Chandler, Sep 27 2006 *)
For prime(2) = 3, 2+3+5 = 10, 3+5+7 = 15, 5+7+11 = 23, 7+11+13 = 31. So a(2) = 23, the first prime that is the sum of 3 consecutive primes.
\\ First prime in the sum of a prime number of consecutive primes
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)*/}
from sympy import isprime, nextprime, prime, primerange
def a(n):
pn = prime(prime(n))
smallest = list(primerange(2, pn+1))
while not isprime(sum(smallest)):
pn = nextprime(pn)
smallest = smallest[1:] + [pn]
return sum(smallest)
print([a(n) for n in range(1, 42)]) # Michael S. Branicky, May 23 2021