A073071 Least k such that k! > prime(1)*prime(2)*...*prime(n) where prime(n) is the n-th prime.

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, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 88, 89

Offset: 1

Author

Benoit Cloitre, Aug 17 2002

Keywords

• easy
• nonn

Comments

If the greater than sign in the definition is replaced by >=, we get A048964. - R. J. Mathar, May 01 2008

Examples

			n=1: prime(1) = 2, 3! > 2, a(1) = 3.
n=2: prime(1)*prime(2) = 6, 4! > 6, a(2) = 4.
		

Links

• David Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A048964, A135667.

Programs

Mathematica

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 *)

PARI

a(n) = my(k=1, p=vecprod(primes(n))); while(k! <= p, k++); k; \\ Michel Marcus, Feb 18 2021

Formula

a(n) should be asymptotic to C*n (where 1

Extensions

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

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