

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
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OFFSET

0,3


COMMENTS



LINKS



FORMULA

I conjecture that for n>2 we have n + 1/2 <= a(n)/a(n1) <= 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



KEYWORD

nonn,hard


AUTHOR



EXTENSIONS

Extended from a(6) on by Patrick De Geest, May 29 2001, using A. Booker's 'Nth Prime Page'


STATUS

approved



