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%I #28 Jan 18 2022 10:15:07
%S 6,120,3628800,51090942171709440000
%N Prime-balanced factorials: factorials k! that are the mean of their 2 closest neighboring primes.
%C Values of k are in A053709.
%F k! = (p+q)/2; p = k! + d, q = k! - d, where p and q are the closest primes to k!.
%F a(n) = A053709(n)!.
%e For k=21, k!=51090942171709440000, d=31, and the closest primes to 21! are q = 21! - 31 = 51090942171709439969, p = 21! + 31 = 51090942171709440031.
%Y Cf. A033932, A033933, A006990, A037151, A006562, A053709.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 10 2000
%E The next two terms are 171! and 190!. - _Jud McCranie_, Jul 04 2000
%E a(3) corrected by _Sean A. Irvine_, Jan 14 2022
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