%I #38 Feb 20 2021 13:29:19
%S 2,3,5,6,7,8,10,11,12,14,15,16,17,19,20,21,23,24,25,27,28,29,31,32,33,
%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 64,66,67,68,70,71,72,73,75,76,77,79,80,81,83,84,85,86,88,89,90,92,93
%N a(n) is smallest number k such that k! >= n-th primorial number (A002110(n)).
%C If in the definition '>=' is replaced by '>' we get A073071. - _Bernard Schott_, Feb 20 2021
%H Giovanni Resta, <a href="/A048964/b048964.txt">Table of n, a(n) for n = 1..10000</a>
%e 9! = 362880 < A002110(7) = 2*3*5*7*11*13*17 = 510510 <= 10! = 3628800, so a(7)=10. [edited by _Jon E. Schoenfield_, May 13 2018]
%t Primorial[n_] := Product[ Prime[i], {i, n}]; a[n_] := Block[{k = 1}, While[(k!) < Primorial[n], k++ ]; k]; Table[ a[n], {n, 71}] (* _Robert G. Wilson v_, Apr 09 2004 *)
%t Module[{nn=100,pn,k=2},pn=FoldList[Times,Prime[Range[nn]]];Table[ While[ k!< pn[[n]],k++];k,{n,nn}]] (* _Harvey P. Dale_, Dec 12 2018 *)
%o (PARI) a(n) = {my(pr = prod(k=1, n, prime(k)), k = 0); while (k! < pr, k++); k;} \\ _Michel Marcus_, May 14 2018
%Y Cf. A000142, A002110, A073071, A093697.
%K nonn
%O 1,1
%A _Labos Elemer_
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 14 2007