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A061232 Number of primes p with n! < p <= (n+1)!. 5
0, 1, 2, 6, 21, 98, 547, 3556, 26738, 227720, 2170267, 22877331, 264314464, 3320870054, 45076422125, 657316885209, 10247614197601, 170081414212020, 2994059471570761, 55718507205774017, 1092932100469356250, 22536709415953547880, 487361620197926253365 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
First differences of A003604. - Artur Jasinski, Dec 13 2007
LINKS
Andrew R. Booker, The Nth Prime Page
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
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.
MATHEMATICA
Table[PrimePi[(n + 1)! ] - PrimePi[n! ], {n, 0, 15}]
CROSSREFS
Cf. A003604.
Sequence in context: A005638 A249395 A008988 * A020091 A008987 A079129
KEYWORD
nonn,hard
AUTHOR
Amarnath Murthy, Apr 23 2001
EXTENSIONS
Extended from a(6) on by Patrick De Geest, May 29 2001, using A. Booker's 'Nth Prime Page'
a(15) from Robert G. Wilson v, Jan 29 2003
Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar
a(17)-a(18) from Donovan Johnson, Oct 30 2012
a(19)-a(22) from A003604(n+1) - A003604(n) by Jinyuan Wang, Mar 11 2020
STATUS
approved

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Last modified June 20 15:55 EDT 2024. Contains 373526 sequences. (Running on oeis4.)