%I #16 Jul 04 2021 10:44:07

%S 3,4,5,6,7,8,10,11,12,14,15,16,17,19,20,21,23,24,25,27,28,29,31,32,33,

%T 34,36,37,38,40,41,42,44,45,46,47,49,50,51,53,54,55,57,58,59,60,62,63,

%U 64,66,67,68,70,71,72,73,75,76,77,79,80,81,83,84,85,86,88,89

%N Least k such that k! > prime(1)*prime(2)*...*prime(n) where prime(n) is the n-th prime.

%C If the greater than sign in the definition is replaced by >=, we get A048964. - _R. J. Mathar_, May 01 2008

%H David Wilson, <a href="/A073071/b073071.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) should be asymptotic to C*n (where 1<C<3/2).

%e n=1: prime(1) = 2, 3! > 2, a(1) = 3.

%e n=2: prime(1)*prime(2) = 6, 4! > 6, a(2) = 4.

%t Module[{nn=100,prmorl,fctorl},prmolr=FoldList[Times, Prime[Range[ nn]]]; fctorl=Range[nn]!;Table[Position[fctorl,_?(#>prmolr[[n]]&),1,1],{n,70}]]//Flatten (* _Harvey P. Dale_, Jul 04 2021 *)

%o (PARI) a(n) = my(k=1, p=vecprod(primes(n))); while(k! <= p, k++); k; \\ _Michel Marcus_, Feb 18 2021

%Y Cf. A002110, A048964, A135667.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Aug 17 2002

%E Corrected by Peter Pein (petsie(AT)dordos.net), May 01 2008