This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053710 #37 May 08 2025 19:19:55 %S A053710 6,120,3628800,51090942171709440000 %N A053710 Prime-balanced factorials: factorials k! that are the mean of their 2 closest neighboring primes. %C A053710 Values of k are in A053709. %C A053710 The next two terms are 171! and 190!. - _Jud McCranie_, Jul 04 2000 %H A053710 Amiram Eldar, <a href="/A053710/b053710.txt">Table of n, a(n) for n = 1..7</a> %F A053710 k! = (p+q)/2; p = k! + d, q = k! - d, where p and q are the closest primes to k!. %F A053710 a(n) = A053709(n)!. %e A053710 For k = 21, k! = 51090942171709440000, d = 31, and the closest primes to 21! are q = 21! - 31 = 51090942171709439969, p = 21! + 31 = 51090942171709440031. %t A053710 Select[Range[25]!,NextPrime[#]-#==#-NextPrime[#,-1]&] (* _Harvey P. Dale_, May 08 2025 *) %Y A053710 Cf. A033932, A033933, A006990, A037151, A006562, A053709. %K A053710 nonn %O A053710 1,1 %A A053710 _Labos Elemer_, Feb 10 2000 %E A053710 a(3) corrected by _Sean A. Irvine_, Jan 14 2022