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A082277 Smallest prime that is the sum of prime(n) consecutive primes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 29 15:34 EDT 2022. Contains 354913 sequences. (Running on oeis4.)