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A090523
Smallest prime p such that floor(n!/p) is prime, or 0 if no such prime exists.
1
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
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
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