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

1,1

Links

Table of n, a(n) for n=1..41.

Formula

Sum of reciprocals converges to 0.28053...

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

Example

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.

Prog

(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

Crossrefs

Cf. A070281.

Sequence in context: A241099 A338977 A090686 * A289154 A155851 A019267

Adjacent sequences: A082274 A082275 A082276 * A082278 A082279 A082280

Keyword

easy,nonn

Author

Cino Hilliard, May 09 2003

Status

approved