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
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
Programs
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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
A138945 Positive integers not in A132018.
1, 9, 12, 15, 17, 20, 22, 24, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 81, 83, 85, 86, 88, 89, 91, 93, 94, 96, 98, 99, 101, 102, 104, 106, 107, 109, 110, 112, 113, 115, 117, 118, 120, 121, 123
Offset: 1
Comments
The latter remains quite dense in N: up to 1000 only about every 5th number is missing, which motivated to introduce its complement in N*, A138945.
Programs
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PARI
pp=1;k=0;for(n=1,999,pp*=numbpart(n);while(k++!<=pp,print1(k"," )))
Comments