A309789 Numbers n such that -1 + Sum_{k=1..n} prime(k)! is prime, where prime(k) is the k-th prime.

2, 3, 4, 20, 25

Offset

1,1

Comments

The sequence is finite. Proof: for n=112, the sum is 2! + 3! + 5! + ... + 601! + 607! - 1, which is divisible by the next prime, 613. All the factorials of the subsequent primes 613!, 617!, ... are obviously divisible by 613. So after n=112 the sum will always be divisible by 613. And from n=26 to n=112 there are no other primes. So this sequence will not produce any other primes. - Metin Sariyar, Aug 26 2019

Links

Table of n, a(n) for n=1..5.

Example

4 is a term because 2, 3, 5, 7 are the first 4 primes and 2! + 3! + 5! + 7! - 1 = 5167 is prime.

Mathematica

p=-1; lst={}; Do[p+=Prime[n]!; If[PrimeQ[p], AppendTo[lst, n]], {n, 1000}]; lst
Position[Accumulate[Prime[Range[25]]!], _?(PrimeQ[#-1]&)]//Flatten (* Harvey P. Dale, May 03 2021 *)

Prog

(PARI) isok(n) = isprime(sum(k=1, n, prime(k)!) - 1); \\ Michel Marcus, Aug 18 2019

Crossrefs

Cf. A000040, A000142, A002982, A111179, A039716.

Sequence in context: A024632 A300902 A352581 * A012578 A012573 A268349

Adjacent sequences: A309786 A309787 A309788 * A309790 A309791 A309792

Keyword

nonn,fini,full

Author

Metin Sariyar, Aug 17 2019

Status

approved