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A090523
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Smallest prime p such that floor(n!/p) is prime, or 0 if no such prime exists.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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
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MATHEMATICA
| Do[p = 1; While[ !PrimeQ[Floor[n!/Prime[p]]], p++ ]; Print[Prime[p]], {n, 3, 30}] (Propper)
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CROSSREFS
| Cf. A090524.
Sequence in context: A087385 A168278 A090521 * A164314 A156003 A011416
Adjacent sequences: A090520 A090521 A090522 * A090524 A090525 A090526
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 07 2003
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Jun 23 2005
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 07 2007
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