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

1,2

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

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

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

Crossrefs

Cf. A096509-A096523, A000142.

Sequence in context: A309866 A287150 A257109 * A319780 A141647 A366386

Adjacent sequences: A096827 A096828 A096829 * A096831 A096832 A096833

Keyword

nonn

Author

Labos Elemer, Jul 14 2004

Status

approved