A079481 Primes prime(k) such that prime(k)*prime(k+1)+(prime(k)-1)! is prime.

2, 3, 5, 7, 13, 17, 71, 643, 2551

Offset

1,1

Comments

From Jason Yuen, Aug 22 2024: (Start)

2551 corresponds to a probable prime.

a(10) > 10000. (End)

a(10) > 20000. - Michael S. Branicky, Apr 14 2025

Links

Table of n, a(n) for n=1..9.

Example

Let prime(k) be 5, therefore prime(k+1) = 7 and prime(k)*prime(k+1) = 35. (prime(k)-1)! = 4! = 24. 35+24 = 59, which is prime.
Let prime(k) be 2, therefore prime(k+1) = 3 and prime(k)*prime(k+1) = 6. (prime(k)-1)! = 1! = 1. 6+1 = 7, which is prime.

Prog

(PARI) forprime (p=3, 1000, if (isprime(p*nextprime(p+1)+(p-1)!), print1(p", ")))

Crossrefs

Sequence in context: A342244 A076047 A245640 * A365274 A178766 A362778

Adjacent sequences: A079478 A079479 A079480 * A079482 A079483 A079484

Keyword

nonn,hard,more

Author

Jon Perry, Jan 16 2003

Extensions

a(8)-a(9) from Jason Yuen, Aug 22 2024

Name corrected by Joerg Arndt, Aug 23 2024

a(1) = 2 inserted by Michael S. Branicky, Apr 14 2025

Status

approved