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A061232
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Number of primes p with n! < p <= (n+1)!.
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0
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0, 1, 2, 6, 21, 98, 547, 3556, 26738, 227720, 2170267, 22877331, 264314464, 3320870054, 45076422125, 657316885209, 10247614197601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| First differences of A003604. - Artur Jasinski (grafix(AT)csl.pl), Dec 13 2007
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LINKS
| Andrew R. Booker, The Nth Prime Page
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FORMULA
| I conjecture that for n>2 we have n + 1/2 <= a(n)/a(n-1) <= n + 2/3. If this conjecture is true we have floor(a(n+1)/a(n)) = n - Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 03 2006
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EXAMPLE
| a(3) = 6 as there are 6 primes between 3! = 6 and 4! = 24: 7,11,13,17,19,23; a(4) = 21 as there are 21 primes between 24 and 120.
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MATHEMATICA
| Table[PrimePi[(n + 1)! ] - PrimePi[n! ], {n, 0, 15}]
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CROSSREFS
| Cf. A003604.
Sequence in context: A001928 A005638 A008988 * A020091 A008987 A079129
Adjacent sequences: A061229 A061230 A061231 * A061233 A061234 A061235
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KEYWORD
| nonn,hard
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 23 2001
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EXTENSIONS
| Extended from a(6) on by Patrick De Geest (pdg(AT)worldofnumbers.com), May 29 2001, using A. Booker's 'Nth Prime Page'.
a(15) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 29 2003
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 15 2008 at the suggestion of R. J. Mathar
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