A082277 Smallest prime that is the sum of prime(n) consecutive primes.

5, 23, 53, 197, 233, 691, 499, 857, 1151, 2099, 2399, 2909, 3821, 4217, 5107, 6079, 10091, 8273, 12281, 11597, 12713, 15527, 22741, 26041, 25759, 37447, 28087, 36607, 36067, 35527, 42463, 46181, 49279, 65033, 67271, 71011, 71167, 76099, 78139, 96001, 95107

Offset: 1

Author

Cino Hilliard, May 09 2003

Keywords

• easy
• nonn

Examples

			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.
		

Crossrefs

Cf. A070281.

Programs

PARI

\\ 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)*/}

Python

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

Formula

Sum of reciprocals converges to 0.28053...

a(n) = A070281(prime(n)). - Michel Marcus, Aug 07 2021