A096830 Number of primes in neighborhood with center=n! and radius = ceiling(log(n!)).

0, 2, 2, 1, 0, 2, 1, 0, 1, 2, 4, 3, 1, 3, 0, 1, 1, 1, 0, 3, 5, 1, 0, 0, 1, 2, 4, 1, 3, 1, 1, 2, 4, 0, 2, 0, 2, 5, 2, 5, 2, 4, 4, 5, 3, 3, 1, 5, 3, 3, 0, 3, 4, 1, 3, 2, 1, 1, 1, 1, 1, 3, 2, 2, 2, 0, 3, 2, 4, 4, 0, 4, 4, 2, 3, 5, 3, 1, 1, 8, 1, 2, 2, 1, 2, 2, 0, 1, 3, 5, 2, 2, 4, 2, 5, 3, 5, 2, 5, 2, 2, 1, 0, 1, 0

Offset: 1

Author

Labos Elemer, Jul 14 2004

Keywords

• nonn

Examples

			n=8: 8!=40320; radius=11, a(8)=0 because there are no primes in the neighborhood.
		

Crossrefs

Cf. A096509-A096523, A000142.

Programs

Mathematica

{ta=Table[0, {1000}], u=1}; Do[s=Count[Table[PrimeQ[n!+i], {i, -Ceiling[Log[n! ]//N], Ceiling[Log[n! ]//N]}], True]; Print[{n, s}];ta[[u]]=s;u=u+1, {n, 1, 1000}];ta

Formula

a(n) = A096509(n!) = A096509(A000142(n)).