A151894 Numbers k such that k! + second prime after k! is prime.

2, 3, 5, 6, 7, 8, 11, 17, 42, 66, 76, 93, 139, 157, 226, 290, 415, 522, 774, 794, 1947

Offset

1,1

Comments

Because numbers of the form (k! + prime) are divisible by all primes <= k that means that the first prime number can have the form k! + next prime after k! and no primes of the form k! + m for m > 1 and m < next prime after k!.

Links

Table of n, a(n) for n=1..21.

Mathematica

a = {}; Do[If[PrimeQ[n! + NextPrime[n!, 2]], AppendTo[a, n]], {n, 1, 200]; a

Prog

(PARI) is(k) = {my(f = k!); isprime(f + nextprime(nextprime(f + 1) + 1)); } \\ Amiram Eldar, Oct 23 2024

Crossrefs

Cf. A002981, A151892, A151893, A151903.

Sequence in context: A191167 A006431 A285528 * A352328 A028229 A104452

Adjacent sequences: A151891 A151892 A151893 * A151895 A151896 A151897

Keyword

nonn,more

Author

Artur Jasinski, Apr 12 2008

Extensions

a(15)-a(20) from Amiram Eldar, Oct 23 2024

a(21) from Michael S. Branicky, Oct 24 2024

Status

approved