|
|
A073071
|
|
Least k such that k! > prime(1)*prime(2)*...*prime(n) where prime(n) is the n-th prime.
|
|
8
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
If the greater than sign in the definition is replaced by >=, we get A048964. - R. J. Mathar, May 01 2008
|
|
LINKS
|
|
|
FORMULA
|
a(n) should be asymptotic to C*n (where 1<C<3/2).
|
|
EXAMPLE
|
n=1: prime(1) = 2, 3! > 2, a(1) = 3.
n=2: prime(1)*prime(2) = 6, 4! > 6, a(2) = 4.
|
|
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 *)
|
|
PROG
|
(PARI) a(n) = my(k=1, p=vecprod(primes(n))); while(k! <= p, k++); k; \\ Michel Marcus, Feb 18 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected by Peter Pein (petsie(AT)dordos.net), May 01 2008
|
|
STATUS
|
approved
|
|
|
|