A090523 Smallest prime p such that floor(n!/p) is prime, or 0 if no such prime exists.

0, 0, 2, 7, 7, 19, 29, 17, 107, 29, 151, 67, 101, 31, 43, 163, 59, 31, 41, 173, 79, 167, 73, 233, 107, 73, 29, 43, 1259, 89, 317, 191, 349, 541, 199, 173, 577, 89, 373, 997, 197, 773, 1093, 257, 1733, 487, 349, 149, 1511, 2621, 389, 181, 151

Offset

1,3

Comments

Conjecture: There are no zeros for n > 2.

This conjecture is correct. For m > 1, there is always a prime between m and 2*m. Taking m = n!/4, this gives us a prime p such that floor(n!/p) = 2 or 3. - Franklin T. Adams-Watters, Jul 28 2011

Links

Table of n, a(n) for n=1..53.

Mathematica

Do[p = 1; While[ !PrimeQ[Floor[n!/Prime[p]]], p++ ]; Print[Prime[p]], {n, 3, 30}] (* Ryan Propper, Jun 23 2005 *)

Crossrefs

Cf. A090524.

Sequence in context: A267499 A351583 A090521 * A164314 A156003 A306417

Adjacent sequences: A090520 A090521 A090522 * A090524 A090525 A090526

Keyword

nonn

Author

Amarnath Murthy, Dec 07 2003

Extensions

More terms from Ryan Propper, Jun 23 2005

More terms from Stefan Steinerberger, Jun 07 2007

Status

approved