A053710 Prime-balanced factorials: factorials k! that are the mean of their 2 closest neighboring primes.

6, 120, 3628800, 51090942171709440000

Offset: 1

Author

Labos Elemer, Feb 10 2000

Keywords

• nonn

Comments

Values of k are in A053709.

The next two terms are 171! and 190!. - Jud McCranie, Jul 04 2000

Examples

			For k = 21, k! = 51090942171709440000, d = 31, and the closest primes to 21! are q = 21! - 31 = 51090942171709439969, p = 21! + 31 = 51090942171709440031.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..7

Crossrefs

Cf. A033932, A033933, A006990, A037151, A006562, A053709.

Programs

Mathematica

Select[Range[25]!,NextPrime[#]-#==#-NextPrime[#,-1]&] (* Harvey P. Dale, May 08 2025 *)

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)!.

Extensions

a(3) corrected by Sean A. Irvine, Jan 14 2022