close
login
A053710
Prime-balanced factorials: factorials k! that are the mean of their 2 closest neighboring primes.
6
6, 120, 3628800, 51090942171709440000
OFFSET
1,1
COMMENTS
Values of k are in A053709.
The next two terms are 171! and 190!. - Jud McCranie, Jul 04 2000
LINKS
FORMULA
k! = (p+q)/2; p = k! + d, q = k! - d, where p and q are the closest primes to k!.
a(n) = A053709(n)!.
EXAMPLE
For k = 21, k! = 51090942171709440000, d = 31, and the closest primes to 21! are q = 21! - 31 = 51090942171709439969, p = 21! + 31 = 51090942171709440031.
MATHEMATICA
Select[Range[25]!, NextPrime[#]-#==#-NextPrime[#, -1]&] (* Harvey P. Dale, May 08 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 10 2000
EXTENSIONS
a(3) corrected by Sean A. Irvine, Jan 14 2022
STATUS
approved