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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 Table of n, a(n) for n=0..22. 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 Adjacent sequences: A061229 A061230 A061231 * A061233 A061234 A061235 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.)