%I A061232
%S A061232 0,1,2,6,21,98,547,3556,26738,227720,2170267,22877331,264314464,
%T A061232 3320870054,45076422125,657316885209,10247614197601
%N A061232 Number of primes p with n! < p <= (n+1)!.
%C A061232 First differences of A003604. - Artur Jasinski (grafix(AT)csl.pl), Dec 
               13 2007
%H A061232 Andrew R. Booker, <a href="http://primes.utm.edu/nthprime/">The Nth Prime 
               Page</a>
%F A061232 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
%e A061232 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.
%t A061232 Table[PrimePi[(n + 1)! ] - PrimePi[n! ], {n, 0, 15}]
%Y A061232 Cf. A003604.
%Y A061232 Sequence in context: A001928 A005638 A008988 this_sequence A020091 A008987 
               A079129
%Y A061232 Adjacent sequences: A061229 A061230 A061231 this_sequence A061233 A061234 
               A061235
%K A061232 nonn,hard
%O A061232 0,3
%A A061232 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 23 2001
%E A061232 Extended from a(6) on by Patrick De Geest (pdg(AT)worldofnumbers.com), 
               May 29 2001, using A. Booker's 'Nth Prime Page'.
%E A061232 a(15) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 29 2003
%E A061232 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 15 2008 at 
               the suggestion of R. J. Mathar