A151903 a(n) = smallest number k such that n! + k-th prime after n is prime.

1, 1, 1, 1, 1, 1, 1, 5, 3, 1, 2, 5, 13, 2, 8, 3, 4, 5, 16, 2, 3, 3, 16, 23, 4, 8, 6, 10, 38, 18, 20, 11, 1, 14, 7, 21, 52, 2, 13, 4, 5, 12, 6, 1, 38, 12, 36, 1, 8, 3, 43, 1, 4, 32, 4, 19, 12, 45, 45, 41, 118, 14, 40, 1, 26, 43, 2, 4, 13, 15, 128, 6, 1, 20, 29, 9, 14, 9, 36, 6, 104, 9, 14, 26, 9

Offset: 1

Author

Artur Jasinski, Apr 12 2008

Keywords

• nonn

Comments

Because numbers of the form : (n! + prime) are divisible by all primes <= n that mean that first prime number can have form n! + k-th prime after n and no primes of the form n! + k for k > 1 and k < next prime after n

Links

• Amiram Eldar, Table of n, a(n) for n = 1..402

Crossrefs

Cf. A002981, A151892, A151894, A151893, A139213, A139214.

Programs

Mathematica

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